How Useful is the Information Ratio to Evaluate the Performance of Portfolio Managers? 9783836634472, 9783836684477

Citation preview

Christoph Schneider

How Useful is the

Information Ratio

Copyright © 2010. Diplomica Verlag. All rights reserved.

to Evaluate the Performance of Portfolio Managers?

Diplomica Verlag

Christoph Schneider How Useful is the Information Ratio to Evaluate the Performance of Portfolio Managers? ISBN: 978-3-8366-3447-2 Herstellung: Diplomica® Verlag GmbH, Hamburg, 2010

Copyright © 2010. Diplomica Verlag. All rights reserved.

Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes der Bundesrepublik Deutschland in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechtes. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Die Informationen in diesem Werk wurden mit Sorgfalt erarbeitet. Dennoch können Fehler nicht vollständig ausgeschlossen werden und der Verlag, die Autoren oder Übersetzer übernehmen keine juristische Verantwortung oder irgendeine Haftung für evtl. verbliebene fehlerhafte Angaben und deren Folgen. © Diplomica Verlag GmbH http://www.diplomica-verlag.de, Hamburg 2010

Fund Performance Measurement

Table of Contents List of Figures..................................................................................................................ii List of Tables ..................................................................................................................iii List of Abbreviations .....................................................................................................iv 1 Introduction ...............................................................................................................1 1.1

Motivation and Objective...................................................................................1

1.2

Course of the Investigation ................................................................................3

2 Theoretical Overview ................................................................................................5 2.1

Methods of Fund Performance Measurement ....................................................5 2.1.1 Characteristics of a Reliable Performance Measure .............................5 2.1.2 The Treynor Ratio .................................................................................6 2.1.3 The Sharpe Ratio...................................................................................7 2.1.4 Jensen’s Alpha ......................................................................................8 2.1.5 The Sortino Ratio ..................................................................................9 2.1.6 The M² Measure ..................................................................................10 2.1.7 The Omega Measure ...........................................................................11

2.2

The Information Ratio......................................................................................12

2.3

Sources of Active Returns: How to Beat the Benchmark ................................15

2.4

Agency Problems Related to Performance Measures ......................................17

3 Data Description and Sources ................................................................................19 3.1

Mutual Fund Selection .....................................................................................19

3.2

Benchmark Selection .......................................................................................24

3.3

Descriptive Statistics........................................................................................26

Copyright © 2010. Diplomica Verlag. All rights reserved.

4 Empirical Study on Selected Performance Measures ..........................................28 4.1

Is the Information Ratio a Reliable Measure of Performance?........................28

4.2

The Information Ratio Versus Other Measures ...............................................33

4.3

The Art of Selecting the Benchmark................................................................40

4.4

Does Data Frequency Matter?..........................................................................43

4.5

Other Influences on Performance Measures ....................................................45

4.6

Performance Persistence: Outperformance by Luck or Skill? .........................48

4.7

Summary of Empirical Results ........................................................................51

5 A Practical View on Performance Measurement .................................................55 6 Conclusion ................................................................................................................60 List of References ..........................................................................................................65 Appendix A ....................................................................................................................71 Appendix B ....................................................................................................................82 i

Fund Performance Measurement

List of Figures Figure 1: Investment Opportunity Set Based on Information Ratios............................. 14 Figure 2: Index Development of Several Security Types .............................................. 26 Figure 3: Box Plots of Equity US and Equity Germany Fund Information Ratios ....... 32 Figure 4: Selected Performance Measures for Equity US Funds................................... 34 Figure 5: Fund Rankings of Selected Performance Measures ....................................... 36 Figure 6: Fund Rankings Using Modified Information Ratios ...................................... 38 Figure 7: Factor Decomposition of Rankings Based on Information Ratios................. 39 Figure 8: Development of Major Large Cap US Equity Indices ................................... 41 Figure 9: The Effect of Benchmark Selection on the Information Ratio....................... 41 Figure 10: Ranking Differences Caused by Different Benchmarks .............................. 43 Figure 11: Comparison of Rankings Based on Different Data Frequencies.................. 45 Figure 12: Performance Persistence of Equity US Funds.............................................. 49 Figure 13: Framework for Performance Evaluation – Year 2008 ................................. 54 Figure 14: Active Share Versus Tracking Error ............................................................ 54

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 15: Distribution of Information Ratios Based on Different Data Frequencies... 71

ii

Fund Performance Measurement

List of Tables Table 1: Sample Size of the Fund Dataset Grouped by Fund Classification .................23 Table 2: Overview of Benchmark Indices .....................................................................24 Table 3: Descriptive Statistics of Fund Returns.............................................................27 Table 4: Information Ratios of Different Fund Categories............................................29 Table 5: Test Statistics for the Difference of Threshold Values of Equity US Funds ...30 Table 6: Test Statistics for the Difference of Threshold Values of US Funds...............31 Table 7: Inconsistency of the Information Ratio for Negative Alphas ..........................37 Table 8: z-Statistics for Significant Difference of the Information Ratios ....................42 Table 9: Information Ratios in Relation to Fund Launch Years....................................47 Table 10: Number of Top 25% Ranks over Lifetime ....................................................50 Table 11: Performance Persistence of Equity US Funds Over Time.............................51 Table 12: Information Ratio – Threshold Values for 1st Quartile Funds (very good) ...72 Table 13: Information Ratio – Threshold Values for 2nd Quartile Funds (good)...........73 Table 14: Test Statistics for Information Ratios of Equity US Funds ...........................74 Table 15: Test Statistics for Information Ratios of Selected US Funds ........................74 Table 16: Distribution Properties of Performance Measures for Equity US Funds.......74 Table 17: Sharpe Ratio – Threshold Values for 1st Quartile Funds (very good) ...........75 Table 18: Sharpe Ratio – Threshold Values for 2nd Quartile Funds (good)...................76 Table 19: Sortino Ratio – Threshold Values for 1st Quartile Funds (very good)...........77 Table 20: Sortino Ratio – Threshold Values for 2nd Quartile Funds (good)..................78 Table 21: Correlation of the Information Ratio With Other Performance Measures ....79 Table 22: Return Distribution of the S&P 500 Index (Timeframe: 1998 until 2008)....79 Table 23: Performance Persistence of Equity and Equity Small Cap Funds .................80

Copyright © 2010. Diplomica Verlag. All rights reserved.

Table 24: Performance Persistence of Corporate Bond Funds ......................................81

iii

Fund Performance Measurement

Copyright © 2010. Diplomica Verlag. All rights reserved.

List of Abbreviations CAPM

Capital Asset Pricing Model

CPPI

Constant Proportion Portfolio Insurance

DAX

Deutscher Aktienindex

EUR

Euro

GBP

British pound

GER

Germany

IC

Information Coefficient

IR

Information Ratio

ISIN

International Security Identification Number

LIBOR

London Interbank Offered Rate

LGC

Lipper Global Classification

MAR

Minimum Acceptable Return

mIR

Modified Information Ratio

MSCI

Morgan Stanley Capital International

REIT

Real Estate Investment Trust

SoR

Sortino Ratio

SR

Sharpe Ratio

TC

Transfer Coefficient

TE

Tracking Error

TR

Treynor Ratio

UK

United Kingdom

US

United States of America

USD

United States dollar

iv

Fund Performance Measurement

1

Introduction

1.1

Motivation and Objective “I do not want a good General, I want a lucky one.” (Napoleon Bonaparte)

In contrast to Napoleon, investors typically do not want to pick a lucky person to administer their funds, but both Napoleon and the investor face a similar problem: how to separate the lucky from the skilled. Historic data shows that five out of one hundred portfolio managers achieve an outstanding performance just by luck, and statistics also reveal that luck – in most cases – does not persist over time. The lucky managers will, however, always cite their superior skills as a reason for their success, while the unsuccessful ones will place the blame on bad luck. By assessing all active managers on the two dimensions luck and skill, four groups are created. The separation of the skilled and lucky from the unskilled but lucky managers and the separation of the skilled but unlucky from the unskilled and unlucky managers is of special interest to all stakeholders in the investment industry. It is, therefore, the investor’s task to apply understandable guidelines, preferably on a quantitative basis, when it comes to evaluating a portfolio manager. On the other hand, it is the fund administration’s task to judge the performance of its managers objectively and to transfer the results into a variable remuneration scheme or to decide about the replacement of a certain manager. (Grinold & Kahn, 2000, pp. 478-480) The idea of comparing the performance of different risky investments, for example investment funds, on a quantitative basis dates back to the beginnings of the asset management industry and has been an important field of research in finance since then (Jen-

Copyright © 2010. Diplomica Verlag. All rights reserved.

sen, 1968, p. 389). Performance measures serve as valuable quantitative evidence for the portfolio manager’s performance as well as for the evaluation of investment decisions ex post (Treynor, 1965, p. 63). Based on the idea of the capital asset pricing model (CAPM) proposed by Treynor (1961), Sharpe (1964), and Lintner (1965), Treynor (1965) developed the first quantitative performance measure intended to rate mutual funds, the Treynor Ratio. Since then, a large number of performance measures with very different characteristics have been developed, for example by Sharpe (1966), Jensen (1968), Treynor & Black (1973), Sortino & Price (1994), and Israelsen (2005). In addi1

Fund Performance Measurement

tion to their power of rating investments ex post, their ability to predict future performance has been thoroughly analyzed by Grinblatt & Titman (1992), Brown & Goetzmann (1995), Carhart (1997), and others. Besides academia, the driving force behind the development of more sophisticated performance measures has always been the investors. This is understandable, as “the truly poor managers are afraid, the unlucky managers will be unjustly condemned, and the new managers have no track record. Only the skilled (or lucky) managers are enthusiastic” (Grinold & Kahn, 2000, p. 478). By combining and applying the results of previous research to a new sample of nearly 10,000 mutual funds that invest in different countries and asset classes, this thesis clarifies its central research question: Is the Information Ratio a useful and reliable performance measure? In order to answer this central question, it has been split up into the following sub-parts: What are the characteristics of a useful and reliable performance measure? What actually is “good” performance? Is the “good” performance a result of luck or of skilled decisions and does it persist over time? How does the Information Ratio compare to other performance measures, and what are its strengths and weaknesses? This empirical study aims at answering all of these questions and provides a framework for performance evaluation by use of the Information Ratio. The Information Ratio, developed in 1973 by Treynor & Black, is one of the most important performance measures in the investment management industry (Grinold, 1989, p. 31). It is a ratio for the excess return of a portfolio relative to a specified benchmark divided by the volatility of the excess returns. The measure, therefore, is able to show how much additional return has been generated per unit of additional risk, which is important information in the field of active management (Treynor & Black, 1973). Besides the interesting characteristics of the Information Ratio, it is of special interest because it is founded on two different theoretical frameworks. While the first framework goes

Copyright © 2010. Diplomica Verlag. All rights reserved.

back to the founders of the Information Ratio, the second framework closely connects it to the fundamental law of active management, which was developed by Grinold (1989). The fundamental law of active management is a central framework for active managers and provides insight on how to use the rationale behind the Information Ratio to construct active portfolios for predefined risk budgets. Additionally, the Information Ratio has not yet been analyzed in an extensive empirical study across different asset classes and countries, which is therefore a supplementary motivation for this paper.

2

Fund Performance Measurement

The empirical study is based on return data of nearly 10,000 funds in the timeframe from January 1, 1998 until December 31, 2008 and yields some important results, which are summarized very briefly in this paragraph. Generally, funds have been categorized according to their investment universe in 13 distinct classes, for example “Equity US” or “Money Market EUR”. In order to judge the value of a certain performance measure, a quartile-based grading system with the four categories “very good”, “good”, “below average”, and “poor” has been developed. Threshold values have been calculated that separate the “very good” quartile from the “good” quartile, and so on. Using this method, the threshold values of the Information Ratio are found to vary over time and also across different asset classes, so that it becomes necessary to re-calibrate the framework annually. The quality and reliability of the Information Ratio is dependent on certain factors of the data selection process. Firstly, only one benchmark should be used for all funds in a fund category in order to allow for better comparability and the selection of this benchmark can heavily influence the threshold values. The benchmark should optimally cover a large proportion of the market that is within the investment universe of the respective fund. Secondly, data frequency should be as high as possible, for example, daily or weekly. Monthly data does not accurately represent the true volatility of returns within a calendar year. Thirdly, non-normally distributed fund returns can affect the usability of the Information Ratio. For example, money market funds show strong non-normal returns, and, therefore, cannot be reliably evaluated with the Information Ratio. There are, however, other measures available that take higher moments of return distributions into account. In order to separate lucky managers from skilled ones, the track record plays an important role, as luck generally is not persistent over time. The final framework evaluates the performance of the active manager based on the quartilebased grade of the Information Ratio, penalizes low active weights using an additional measure and incentivizes persistent (skilled) performance by looking at the manager’s Copyright © 2010. Diplomica Verlag. All rights reserved.

track record.

1.2

Course of the Investigation

Following the introduction and the motivation for the topic, Section 2 lays out the theoretical foundations of this paper. Firstly, Sub-section 2.1 explains different methods of fund performance management by describing the characteristics of reliable performance 3

Fund Performance Measurement

measures in part 2.1.1, and continues by presenting six widely-used ratios to evaluate fund performance in the mutual fund industry in parts 2.1.2 to 2.1.7. Each performance measure is explained briefly and its advantages and disadvantages are outlined in order to get a good overview of the rationale behind these measures. As the Information Ratio is at the center of interest of this study, it is explained in detail in Sub-section 2.2. In order to better understand the motivation behind active management, Sub-section 2.3 describes the fundamental law of active management. This leads to a better understanding of the relevant parameters that influence the level of excess returns and clarifies the theoretical framework of the Information Ratio from a different perspective. Subsection 2.4 presents agency problems in the fund management industry in general and special issues that are related to the Information Ratio. Section 3 elaborates on the composition and characteristics of the dataset that is used in the empirical study by explaining the selection of mutual funds (3.1) and benchmark indices (3.2), as well as by showing descriptive statistics of the different fund categories (3.3). The empirical study, which is the central part of this thesis, is presented in Section 4. It starts in Sub-section 4.1 by testing the Information Ratio for stability over time and across different fund categories and continues in Sub-section 4.2 by comparing the ranking order of the Information Ratio against several other performance measures. Sub-sections 4.3 and 4.4 provide information about the robustness of the Information Ratio against the selection of different benchmarks and data frequencies. Other influences that could possibly affect the quality of the Information Ratio, such as nonnormality of returns or survivorship bias inherent in the dataset, are described and analyzed in Sub-section 4.5. In order to separate lucky from skilled managers, the persistency of good Information Ratios over time has been researched in Sub-section 4.6. The

Copyright © 2010. Diplomica Verlag. All rights reserved.

empirical part concludes with a summary and the development of a specific performance evaluation framework detailed in Sub-section 4.7. Section 5 sheds light on the experiences and opinions of several practitioners with respect to performance measurement in general and the use of the Information Ratio in particular. This view will complement the results of the empirical analysis. The thesis concludes with Section 6, where all findings are summarized and starting points for future research are presented. 4

Fund Performance Measurement

2

Theoretical Overview

2.1

Methods of Fund Performance Measurement

2.1.1 Characteristics of a Reliable Performance Measure Before providing an overview of some of the most important performance measures, it is necessary to characterize the properties of a reliable and “good” performance measure. Treynor (1965, p. 64) had two requirements in mind when developing the first performance measure. Firstly, the ratio should provide the same value as long as the performance of the manager does not change, even in unfavorable market conditions. Secondly, the ratio has to incorporate the specific preferences of investors’ risk aversion. According to Hübner (2007, p. 65), there are two factors that determine the quality of a performance measure: stability and precision. A stable measure is robust with respect to the selection of asset pricing models and should not vary strongly in terms of its classification over time, that is if a “very good” Information Ratio is above 0.5, optimally, this should also be true in all subsequent years. Additionally, the performance measure should be precise, which means that it should be able to provide the “true” ranking of funds based on the investor’s preferences. The Information Ratio will be tested on both factors in the empirical part of this paper. Chen & Knez (1996, pp. 511-513) explain that a performance measure has to evaluate the service that is provided to the investor. Does the active manager really “enlarge the investment opportunity set faced by the investing public and, if so, to what extent” (Chen & Knez, 1996, p. 512)? They introduce the idea of an “admissible performance measure”, which is characterized by four criteria. Firstly, the ratio has to assign a performance of zero to the passive benchmark portfolio. Secondly, the ratio has to be a linear function in order to allow for good comparability and to ensure that outperformance can be attributed to superior information. Next, the performance measure has to be continuous so that funds with an equal per-

Copyright © 2010. Diplomica Verlag. All rights reserved.

formance receive the same performance value. Lastly, the function of the ratio has to be nontrivial. As an addition, Chen & Knez (1996, p. 514) prefer measures that assign higher performance values to superior funds and lower performance values to inferior funds. As outlined in detail within the introduction, the development of the first performance measures dates back to the proposal of the CAPM by Treynor (1961), Sharpe (1964) and Lintner (1965). While Treynor (1965) was the first to introduce a meaningful per5

Fund Performance Measurement

formance measure, immediately after, this field of research was extended by Sharpe (1966) and Jensen (1968). The Information Ratio was introduced by Treynor & Black (1973). Other important and widely used measures were developed by Sortino & Price (1994), Modigliani & Modigliani (1997), and Keating & Shadwick (2002). All of these measures are still widely used in the fund management industry, although some of them have been developed more than 40 years ago. Therefore, the measures will be presented and characterized briefly in the following sub-sections (Hübner, 2005, p. 415). As the Information Ratio is in the center of interest of this thesis, it will be explained and analyzed in detail in a separate section (cf. Chapter 2.2).

2.1.2 The Treynor Ratio Treynor (1965) developed the Treynor Ratio (TR) based on the idea of the CAPM that had been proposed just shortly before. Treynor (1965, pp. 64-65) introduces the so called “characteristic line” for each investment fund, which basically is a regression line showing the relationship between the fund’s returns and the benchmark’s returns. The slope of the line is called β and characterizes the fund’s volatility in relation to the volatility of the benchmark. A β = 2.0 for example means that the respective fund will change its rate of return by 2% if the benchmark rate of return changes by 1%. The intercept of the characteristic line is called α and expresses the average outperformance or underperformance of the fund in relation to the benchmark. The Treynor Ratio is defined according to Equation 1: (1)

TR =

rP − rM

β

=

α β

where rP is the return of the fund or portfolio, rM is the return of the benchmark for the respective market and β is the regression beta as explained above. The Treynor Ratio Copyright © 2010. Diplomica Verlag. All rights reserved.

therefore measures relative return in relation to relative risk or, to put it in other words “portfolio performance per unit of systematic risk” (Hübner, 2005, p. 416). While Treynor (1965, p. 69) initially defined rM as the rate of return of the market benchmark, that is a stock index, the ratio has later been calculated with rM equal to zero or the risk-free rate (Hübner, 2005, p. 418). In practical applications the Treynor Ratio is beneficial in cases where investors have to select one out of many actively managed investment funds (Hübner, 2007, p. 65). How6

Fund Performance Measurement

ever, it has certain drawbacks which limit its practical use. Firstly, if the β is close to zero, which can be the case for selected funds, the ratio will go to infinity. Secondly, it is unstable and imprecise for market-neutral funds, such as certain hedge fund strategies. Thirdly, if the β is negative, the ratio even provides positive values for funds with a negative alpha (Hübner, 2005, p. 416, 2007, p. 65).

2.1.3 The Sharpe Ratio Introduced by Sharpe (1966), the Sharpe Ratio (SR), which was initially called rewardto-variability ratio, is meant as an extension of the Treynor Ratio. While Treynor (1965) strived to only evaluate fund performance ex post, Sharpe (1966) explicitly aimed at predicting future performance with his measure and also by using the Treynor Ratio (p. 119). The Sharpe Ratio has been discussed heavily in literature, and its theoretical foundation was also extended twice by the founder in Sharpe (1975) and Sharpe (1994). Using Equation 2, the Sharpe Ratio can be easily calculated: (2)

SR =

rP − r f

σP

where rP is the return of the fund or portfolio, rf is the return of the risk-free rate and σP is the standard deviation of the fund or portfolio. The formula clearly highlights the differences between the Sharpe Ratio and the Treynor Ratio. The Treynor Ratio only considers the systematic part of the risk of a mutual fund but does not take into account the diversifiable risks. In contrast to this, the Sharpe Ratio uses the total risk in its denominator. Therefore, the Sharpe Ratio is also able to highlight the risks inherent in an inappropriately diversified fund (Sharpe, 1966, p. 128). These characteristics advise the use of the Sharpe Ratio if one investment portfolio is to be chosen as the single investment

Copyright © 2010. Diplomica Verlag. All rights reserved.

of a particular investor. In this case, only total risk counts. Therefore, style portfolios will generally not be evaluated by the use of Sharpe Ratios. A style portfolio consists of a defined group of asset that shares similar characteristics, such as value stocks or small cap stocks. These types of funds should not be the core asset within an overall asset allocation strategy and, therefore, not be evaluated with a performance measure that looks at total risk (Hübner, 2007, p. 65). In terms of practical applications, the Sharpe Ratio has several drawbacks. Horowitz (1966) had already discovered that the performance predictability capabilities of this 7

Fund Performance Measurement

ratio were rather limited when correcting for the fund’s objectives. Another problem arises if returns that are used to calculate the Sharpe Ratio are not normally distributed. In this case, it is not possible to easily compare Sharpe Ratios that are based on returns with different distribution characteristics without further adjustments (Mahdavi, 2004, p. 47). A different, yet important, problem can arise from the estimation of returns and volatilities, which are the two input factors of the Sharpe Ratio. Lo (2002) found that the Sharpe Ratio for a hedge fund could be overstated by as much as 65% and provide inaccurate rankings. Additionally, the Sharpe Ratio can provide false rankings if the numerator becomes negative, that is the fund performance is below the risk-free rate (Scholz, 2006, p. 347). Several improvements have been proposed to compensate for this issue by Israelsen (2003; 2005), Scholz & Wilkens (2006), and others. Despite these drawbacks, the Sharpe Ratio is as widely used as it is easy to calculate and provides useful ranking information based on Markowitz’ (1952) mean-variance framework.

2.1.4 Jensen’s Alpha Jensen (1968) introduced the Jensen’s Alpha measure, which is based on the CAPM and closely related to the Treynor Ratio. The Jensen’s Alpha uses the CAPM in order to find the rate of return a portfolio or investment fund should yield based on its beta. The alpha itself is then a measure of outperformance or underperformance relative to the return that would be expected based on the CAPM. Therefore, Jensen’s Alpha only accounts for systematic risk and ignores diversifiable risk. Graphically, the alpha measure is the vertical distance between the fund’s return and the security market line in an expected return/systematic risk diagram (Moy, 2002, p. 227). Jensen’s Alpha can be derived according to Equation (3):

Copyright © 2010. Diplomica Verlag. All rights reserved.

(3)

α = rp − (rf + β P ⋅ [rM − rf ])

where rP is the rate of return of the portfolio or investment fund, βP is the beta of the portfolio, rf is the risk-free rate and rM is the market or benchmark rate of return. In contrast to the Sharpe Ratio, Jensen’s Alpha measures the return above or below the benchmark at the fund’s risk level. The rankings of both measures will therefore differ depending on the level of unsystematic risk inherent in the respective funds. When combining both measures, it is actually possible to find funds with a high level of un8

Fund Performance Measurement

systematic risk as these funds will show low Sharpe Ratios but high alpha measures (Moy, 2002, pp. 227-228). These funds lack diversification. Although the alpha measure is quite popular in practice, it has some major weaknesses (Grinblatt & Titman, 1993, p. 47). According to Kothari & Warner (2001), the power of this measure is quite low as the CAPM has been proven not to be true in reality and because it is extremely difficult to detect excess returns when the fund’s style differs from the value-weighted benchmarks. Additionally, the alpha measure is very sensitive to the β and can be misleading if there is little correlation between the fund and the benchmark (Moy, 2002, p. 229). It can also yield biased results when evaluating funds based on market timing strategies (Grinblatt & Titman, 1993, p. 47). Extensions of Jensen’s Alpha use the three factor model proposed by Fama & French (1993) or other assetpricing models, but do also have drawbacks in practical applications (Kothari & Warner, 2001, p. 2009).

2.1.5 The Sortino Ratio

In contrast to the assumptions of standard portfolio theory, investors do not judge upside-risk and downside-risk equally. Logically, all investors prefer positive over negative returns but the widely used standard deviation measure does not differentiate between positive volatility (leading to additional positive returns) and negative volatility (leading to additional negative returns). Both movements are weighted equally, although this is not consistent with the investor’s preferences (Estrada, 2006, p. 117). While the idea of adverse volatility had already been proposed by Levy (1968, p. 45), it took decades until Sortino & Price (1994) operationalized this idea and developed the Sortino Ratio (SoR), an extension of the Information Ratio, which will be presented in Section 2.2. Together with the Sortino Ratio, the idea of downside deviation is introCopyright © 2010. Diplomica Verlag. All rights reserved.

duced and explained. Downside deviation is a measure for negative volatility, and it is calculated based only on returns that are below the minimum acceptable return (MAR). All returns above the MAR do not increase the volatility; they actually decrease it (Sortino & Price, 1994, p. 61). The Sortino Ratio can be calculated based on Equation 4: (4)

SoR =

rP − rM

σ down

, where σ down =

1 T 2 ⋅ ∑ [Min(rP ,t − MAR, 0 )] T t =1

9

Fund Performance Measurement

and where rP is the return of the fund or portfolio, rM is the return of the benchmark for the respective market and MAR is the minimum acceptable return. The MAR is often equal to the benchmark’s return (rM) of the same period or the risk-free rate. The σdown is simply the downside deviation that was mentioned previously. Compared to the Information Ratio, the Sortino Ratio is the same except that the tracking error volatility is calculated based only on returns that are below the minimum acceptable return. In terms of practical applications, the Sortino Ratio can be unreliable or impossible to calculate if there are no or only very few returns below the MAP within the observation period. This could lead to the denominator being equal to zero in an extreme case or to a false estimate of the downside risk if there are only few returns below the MAP present. On the positive side, Chaudhry & Johnson (2008) found that the Sortino Ratio actually is a measure with high predictive power when it comes to returns that are positively skewed. Pedersen & Satchell (2002) came to a similar conclusion for asymmetric returns in general.

2.1.6 The M² Measure

Based on the idea of the Sharpe Ratio, Modigliani & Modigliani (1997) developed the M² performance measure or the measure of risk-adjusted performance. While the interpretation of the value of most other performance measure, including the Sharpe Ratio, on a stand-alone basis is difficult and lacks intuition, Modigliani & Modigliani (1997) overcome this difficulty. Their measure adjusts the risk (standard deviation) of an investment portfolio by mixing it with the risk-free rate so that it exactly matches the standard deviation of the respective benchmark, which in most cases is a market index. This adjustment allows the investor to actually compare the outperformance or underperformance of a particular fund versus its benchmark on a risk-adjusted basis. This Copyright © 2010. Diplomica Verlag. All rights reserved.

means, the M² measure can be directly interpreted as risk-adjusted outperformance (for positive M²) or underperformance (for negative M²) in terms of percentage points. It, therefore, supports the economic intuition of investors and is easily understood (Modigliani & Modigliani, 1997, pp. 45-47). The M² measure is calculated according to Equation 5: (5) 10

⎡ σ M 2 = ⎢r f + (rP − r f )⋅ M σP ⎣

⎤ ⎥ − rM ⎦

Fund Performance Measurement

where rf is the rate of return of the risk-free asset, rP is the rate of return of the portfolio or fund, rM is the return of the benchmark, σM is the standard deviation of the benchmark, and σP is the standard deviation of the portfolio or fund. According to Muralidhar (2000, p. 64) there are four different categories of funds to be distinguished: funds showing outperformance on an absolute and risk-adjusted basis, funds showing outperformance only on an absolute basis, funds showing underperformance on an absolute and risk-adjusted basis, and funds showing underperformance only on an absolute basis. Only funds that can be classified into the first category are really superior to an investment into the benchmark.

2.1.7 The Omega Measure

The Omega Measure introduced by Keating & Shadwick (2002) is a relatively new measure within the field of performance measurement. It is the only measure being presented within this thesis that is able to correctly deal with non-normally distributed returns and does not require any kind of utility function in order to correctly rank different mutual funds by investors’ preferences. Omega is directly based on the cumulative distribution function of the returns and is therefore able to incorporate all higher moments of this distribution. The ratio introduces a loss threshold and weights possible gains or losses relative to this threshold by their probability. Equation 6 formalizes this relationship: b

(6)

Ω(l ) =

∫ [1 − F (x )] dx l

l

∫ F (x ) dx a

where F(x) is the antiderivative of the cumulative distribution function of the returns Copyright © 2010. Diplomica Verlag. All rights reserved.

that is defined in the interval between [a, b] and l is the loss threshold that has to be specified exogenously (Keating & Shadwick, 2002, p. 71). In order to rank different funds, their Omega Measure has to be calculated for a given loss threshold. The fund with the highest ratio is considered the best fund – it has the highest probability for returns above the threshold. However, the ranking order can change for different loss thresholds (Keating & Shadwick, 2002, p. 78). Additional research has yet to be per-

11

Fund Performance Measurement

formed in order to judge the advantages and disadvantages of this measure in the empirical environment.

2.2

The Information Ratio

“The information ratio is an important – perhaps the single most important – measure of investment performance. Investment managers will desire to have an investment strategy with the highest possible information ratio.” (Grinold, 1989, p. 31) As indicated by Grinold’s (1989) quote, the Information Ratio (IR) is a popular and widely used performance measure. It was developed by Treynor & Black (1973) and initially called “appraisal ratio”. The Information Ratio indicates how much additional excess return over the benchmark can be obtained per additional unit of residual risk. Therefore, it is able to quantify how much value is added or destroyed by the active manager. As an example, the active manager usually has some expectations about future stock price developments. He will use this information to overweight or underweight certain stocks relative to the market portfolio, and thereby incur additional risks (relative to the market). Through the use of the Information Ratio, the investor is able to see how much additional return has been generated by the active manager in relation to the additional risks he had to incur in order to implement his superior information by overweighting or underweighting certain stocks. This is also the reason why this ratio is called Information Ratio – it measures the quality of the manager’s superior information (Goodwin, 1998, pp. 34-35). According to Treynor & Black (1973), the Information Ratio can be calculated as shown in Equation 7:

Copyright © 2010. Diplomica Verlag. All rights reserved.

(7)

IR =

rP − rM

σ ER

=

α ω

where rP is the rate of return of the portfolio or fund, rM is the return of the benchmark and σER is the volatility of the excess return, that is the standard deviation of the α. The rationale behind the Information Ratio is very closely related to the investor’s utility function as shown by Jacobs & Levy (1996, p. 12). They explain that investors of active funds are not risk-averse in the common sense but rather regret-averse. Regret-aversion means that they generally accept the risk of a passive investment in this asset class but – 12

Fund Performance Measurement

depending on the excess returns of the active fund – regret their decision to invest in an active fund and not in the passive alternative. According to the derivation of Jacobs & Levy (1996, p. 12), the utility of the investor rises with increasing excess returns and decreases with increasing residual risk. The relationship between residual risk and utility depends on to the investor’s individual regret aversion. Equation 8 mathematically illustrates the utility function: (8)

(

U = α − λ ⋅ω 2

)

where U is the investor’s utility, α is the excess return, λ is the regret-aversion coefficient and ω is the residual risk. Based on this idea, investors are able to use the Information Ratio or, to be precise, the residual risk measure in order to limit the fund universe based on their personal risk preferences. Alternatively, the investor can restrict the active manager by setting a maximum residual risk limit that he is willing to bear. In practice, the residual risk is sometimes called tracking error volatility or simply tracking error. In this study, the term tracking error always refers to tracking error volatility, that is the residual risk or the standard deviation of the excess returns. Investors should, however, be aware that restrictions in terms of tracking error can lead to losses in overall utility (Israelsen & Cogswell, 2007, pp. 419-420; Jacobs & Levy, 1996, p. 13). The term tracking error can be misleading and would be better changed into “differential from benchmark” according to Israelsen & Cogswell (2007), as a high tracking error is not negative per se. They found within their study that funds with a low tracking error show a higher beta, similar standard deviation and lower alpha when compared to funds with high tracking errors (Israelsen & Cogswell, 2007, p. 424). Grinold & Kahn (2000) had previously proposed the ex-ante use of the Information Ratio for risk budgeting purposes. Figure 1 shows the portfolio possibility lines for different target Information Ratios in an excess return/residual risk framework. It can be stated that different Infor-

Copyright © 2010. Diplomica Verlag. All rights reserved.

mation Ratios allow for different opportunities. While Portfolio 1 is only achievable for a fund with a target ratio of 1.0, Portfolio 2 can be reached with a lower target ratio of 0.5. Based on this framework, the portfolio manager can only increase his alpha by increasing the tracking error for a given target Information Ratio (Grinold & Kahn, 2000, pp. 118-119).

13

Fund Performance Measurement

Figure 1: Investment Opportunity Set Based on Information Ratios 10,0%

Excess Return

8,0%

IR = 0.50 IR = 0.75 IR = 1.00

Portfolio 1

6,0%

4,0% Portfolio 2 2,0%

0,0% 0,0%

2,0%

4,0%

6,0%

8,0%

10,0%

Residual Risk

Source: Adapted from Grinold & Kahn (2000, p. 118)

In terms of applications, the Information Ratio is used when it comes to selecting an actively managed portfolio for an investor who currently holds passive portfolios, such as index funds (Hübner, 2007, p. 65). It is also important to note that the Information Ratio does not provide any guidance with respect to asset allocation decisions. An actively managed bond fund with an Information Ratio of 0.5 is not automatically inferior to an actively managed equity fund with an Information Ratio of 1.0, as the measure does not incorporate correlations and levels of risk tolerance of the investor. Therefore, it should only be used to compare investment portfolios within the same style and asset universe (Goodwin, 1998, p. 41). However, Grinold & Kahn (2000, p. 114) mention that according to their research a top quartile manager has an Information Ratio of 0.5 and an exceptional manager should achieve a value of 1.0 or above. They believe this classification is true for all asset classes and time horizons with only slight deviations. Jacobs & Levy (1996, p. 12) also found an Information Ratio of 0.5 or above to be “very good” without restrictions to asset classes. Goodwin (1998, p. 41) analyzed the

Copyright © 2010. Diplomica Verlag. All rights reserved.

distribution of Information Ratios for samples of funds with different investment universes and found significantly different results across fund categories. This seems to be more plausible than the findings of both other studies and therefore different ranges of Information Ratios are expected in the empirical analysis when evaluating funds that invest in different asset classes and countries.

14

Fund Performance Measurement

2.3

Sources of Active Returns: How to Beat the Benchmark

A general issue in the field of active portfolio management is the identification of sources for excess returns above the benchmark, the so-called alpha. While this paper cannot elaborate on this topic in detail, it was found to be essential to present the key concepts. As will be explained later in this section, the Information Ratio is very closely related to two determinants of active returns. This section will improve the theoretical understanding of the Information Ratio as well as explain the rationale behind actively managed funds. Grinold (1989) developed the fundamental law of active management, a framework for active managers that is well known in the fund management industry (Staub, 2007, p. 358). Grinold & Kahn (2000) explain that investors select among different opportunities based on their personal preferences, which for actively managed funds “point toward high residual return and low residual risk” (p. 5). This concept, in fact, is very closely related to the theory of the Information Ratio (cf. Chapter 2.2) and also an important part of the theoretical fundament of this paper. Achieving high Information Ratios is not only favorable in terms of performance measurement, but also closely related to successful active management. To put it in other words, successful active managers will automatically achieve superior Information Ratios and the input factors of the Information Ratio can provide valuable guidance when taking investment decisions. Grinold (1989) identified two factors that lead to high Information Ratios. The first factor is the skill of the manager to correctly predict the residual return of each security in his investment universe. This factor is called the Information Coefficient (IC) and measures the correlation between the actual alpha and the forecasted alpha. If a manager is always right in his forecasts, he will achieve an IC of 1, while a manager without any skill will get an IC of 0 (Wander, 2003, p. 37). The second factor describes the number of inde-

Copyright © 2010. Diplomica Verlag. All rights reserved.

pendent investment decisions that are taken per year and is called breadth. Clearly, if a highly skilled manager takes 100 (in contrast to 10) investment decisions per year, his Information Ratio should and actually will be higher (Grinold & Kahn, 2000, pp. 147150). The fundamental law of active management illustrates the relationship between Information Ratio, Information Coefficient, and breadth to be as follows: (9)

IR ≈ IC ⋅ breadth

15

Fund Performance Measurement

where IR is equal to the Information Ratio and IC symbolizes the Information Coefficient. It should be noted that this relationship is only an approximation. As illustrated by Equation 9, the Information Ratio can be doubled by doubling the IC, that is the skill of the manager; by quadrupling the breadth, that is the number of independent investment decisions; or by using a combination of both actions (Grinold & Kahn, 2000, p. 148). However, the crucial point is the correct forecasting of residual returns, which should be a key skill of all active managers. Quantitative or qualitative models may be used in order to predict future returns. While some managers specialize in security selection of US equities, for example, other managers are good at forecasting returns of certain asset classes. Depending on the number of independent bets a manager takes, different skill levels are required in order to achieve a “good” or “very good” Information Ratio (Wander, 2003). Irrespective of Grinold’s (1989) framework, believers of the efficient markets hypothesis would always question the value added of actively managed funds (Bodie, Kane, & Marcus, 2005, p. 378). Based on the strong form of the efficient markets hypothesis, all information, public and private, is reflected in the current stock prices. Therefore, it is impossible for active managers to add any value. In this case, active returns are generated simply by chance. The semi-strong form of the efficient markets hypothesis suggests that all publicly available information is already incorporated in the current stock prices. In order to generate positive excess returns, active managers would have to have insider information, which would be illegal. Only the weak form of the efficient markets hypothesis, which states that past price information is contained in the current stock prices, would allow active managers to add value by performing economic or fundamental analysis (Grinold & Kahn, 2000, p. 481). While Jensen (1968) and additional researchers in the 1970s suggested that active management was inferior to passive investments, this view changed within the 1980s. It became generally accepted that there Copyright © 2010. Diplomica Verlag. All rights reserved.

were inefficiencies in the market that could be successfully exploited. This is particularly true for markets with lower liquidity like small cap stocks, real estate, alternative investments, and emerging markets. However, when taking fees for active management and tax effects into account, it is today from an academic point of view still unclear whether actively managed funds are able to consistently outperform the market. At least on average they are not able to do so (Baks, Metrick, & Wachter, 2001, pp. 45-46; Malkiel, 1995). This is also confirmed by the empirical results of this paper as presented 16

Fund Performance Measurement

in Section 4. Based on detailed analyses, Wermers (2000) found that active funds were able to outperform the market during 1975 through 1994 by 1.3% per year. On average, 0.6% can be attributed to higher average returns in relation to the characteristics of securities held by a fund, and the remaining 0.7% is due to stock picking abilities. However, when taking fees into account, the active funds underperform the market by 1.0%. Almost 1.6% of the 2.3% return differences is caused by fund expenses and transaction costs. Still, certain drawbacks of passive investments should be kept in mind before taking an investment decision: passive funds will never be able to outperform the market; they are always fully invested (even in severe market conditions), and they modify their holdings to match the benchmark without taking into account any opportunities that might be available in the market (Kjetsaa, 2004, p. 103).

2.4

Agency Problems Related to Performance Measures

The investment management business is a very typical environment in which agency problems in the form of moral hazard can arise. This is due to the fact that the manager is able to easily hide certain information, and monitoring activities are very costly, if not impossible at all for the investor. Therefore, it is crucial to closely align the interest of the fund manager, the agent, with the interest of the principal, the investor, by the use of performance measures and investment guidelines (Golec, 1992, pp. 82-83; Stoughton, 1993, pp. 2009-2010). Initially developed by Ross (1973) and Holmstrom (1979), principal-agent problems are in many cases resolved by introducing variable payment schemes that are designed to increase the agent’s wealth only if the agent acts in the principal’s interest. The simplest form of a performance-based contract utilizes a fixed part, which is paid in all cases, and a variable part, called bonus, that has call option-like characteristics and depends on the level of success of the manager (Grinblatt & Titman,

Copyright © 2010. Diplomica Verlag. All rights reserved.

1989a, pp. 808-809). More complex forms of performance-based compensations include caps on the maximum level of the variable payment, certain trigger levels that have to be reached before a bonus will be paid, and penalties for inferior performance (Grinblatt & Titman, 1989a, pp. 810-811). The implementation of a performance-based payment scheme is the responsibility of the fund administration, which also has to select appropriate performance measures. These actions will help to limit information asymmetries and align the interest of the investors with that of the manager. 17

Fund Performance Measurement

While these general problems are mostly clear at first sight, additional issues can arise because of the use of a particular performance measure. A problem, mainly related to the Information Ratio, will be illustrated based on the fundamental law of active management. In this example, which has been adapted from Grinold & Kahn (2000, pp. 149-150), a target Information Ratio of 0.5 is assumed. This target can be achieved in many different ways; three of them will be illustrated in the following. Firstly, a manager who has market timing skills that result in quarterly information (four per year) about returns of different securities markets will need an IC of 0.25 in order to reach his goal: 0.5 = 0.25 ⋅ 4 . Another manager is good at securities selection. He tracks 100 companies and adjusts his investment fund on a quarterly basis. This manager has to achieve an IC of just 0.025 for an Information Ratio of 0.5: 0.5 = 0.025 ⋅ 400 . A third manager is specialized on two companies and revises his view on each company 200 times a year. The skill level required for this manager will therefore also be 0.025, as he is taking 400 bets every year: 0.5 = 0.025 ⋅ 400 . As outlined above, the Information Ratio assigns all three managers the same Information Ratio and, therefore, equal performance. While this paper does not intend to discuss the efforts and achievements of the three managers in the example, an extreme case scenario in the form of a thought experiment will demonstrate the agency problem. If one imagines a portfolio manager who takes just one active investment decision per year and whose correlation between forecasted and actual returns is 0.1, this manager will achieve an Information Ratio of 0.1: 0.1 = 0.1⋅ 1 . As will be shown in the empirical part of this paper, an Information Ratio of 0.1 for an Equity US fund would in most years be assigned a “good”, and in some years even a “very good” rating, although the manager did practically nothing (cf. Appendix A, Table 12 and Table 13). The Information Ratio can therefore incentivize strategies that are unfavorable to investors. This is also confirmed by Cremers & Peta-

Copyright © 2010. Diplomica Verlag. All rights reserved.

jisto (2007), who found that closet indexers, which are actively managed funds that in fact are taking few active bets or very closely track the benchmark’s weighting of stocks, managed about 30% of all assets in 2003 (p. 3). This is very annoying for investors, as they could buy index funds with lower management fees instead. It seems that performance measures, which use the tracking error as risk measure would need a second dimension that observes the active weights of the fund (Cremers & Petajisto, 2007, p. 8). In order to tackle this issue, Cremers & Petajisto (2007, pp. 6-7) proposed the Active Share measure that is easy to calculate and able to quantify the active holdings of a 18

Fund Performance Measurement

mutual fund in relation to the corresponding benchmark. It is calculated according to Equation (10): (10)

Active Share =

1 N ⋅ ∑ w fund ,i − windex ,i 2 i =1

where wfund,i is the weight of stock i in the fund and windex,i is the weight of stock i in the benchmark index. The Active Share measure will be 0% or 0.0 if the fund’s stock weightings equal the benchmark’s weightings. As mutual funds are not allowed to take short positions, the measure will in this case always be between 0.0 and 1.0. Cremers & Petajisto (2007, pp. 22-23) found that a combination of the Active Share measure and the residual risk or tracking error for performance measurement can significantly increase the alignment of the investor’s interest with the manager’s interest. In general, from an agency theoretic point of view, all performance measures that compare the fund performance against the benchmark performance do incentivize few deviations from the benchmark’s stock weightings. This is due to the fact that active managers fear large negative excess returns which could be a result of significant deviations from the benchmark and which in turn would lower the amount of assets under management (Chan, Chen, & Lakonishok, 2002, p. 1434; Eveillard, 2000).

3

Data Description and Sources

This section describes in detail the fund selection process, descriptive statistics of the dataset and the sources that have been used in order to retrieve the dataset, which is the basis of the empirical analysis in Section 4. As the quality of the dataset is one of the major determinants of the conclusions that will be drawn from the study itself as well as of the reliability and significance of these results, due care must be employed in the data

Copyright © 2010. Diplomica Verlag. All rights reserved.

selection and retrieval process.

3.1

Mutual Fund Selection

While all actively managed and publicly available investment funds were in the scope of the empirical study in this paper, reasonable restrictions had to be set in place due to the extremely large number of investment funds that exist worldwide. According to the Investment Company Institute (2008, p. 158) more than 66,000 different equity mutual funds around the world were available to the public in 2007, including only home-

19

Fund Performance Measurement

domiciled funds. All funds are mainly categorized according to their domicile, countries in which they are registered for sale, and most importantly their investment universe to create homogenous groups for easier comparison. The investment universe generally describes the securities that are investable by the fund manager, for example equity securities, fixed-income securities, money market securities, a mix of the mentioned classes, and even alternative investments such as commodities or real estate. As these classes are usually too broad to be used as an investment universe for a specific fund, additional sub-categories such as equities in Germany, large cap equities, value stocks, or corporate investment grade bonds have been established. Generally, company size and book-to-market ratio are two very commonly used dimensions for the categorization of fund styles (Chan et al., 2002, p. 1434). In fact, some widely regarded classification schemes, such as the Morningstar Fund Categories or the Lipper Global Classification (LGC) have evolved in the fund management industry in the past. Lipper (2005) describes the purpose of the LGC as to create homogeneous groups of funds with comparable investment objectives. Funds within one LGC sector invest in the same financial market(s) or specific segments of those markets, but may adopt different investment strategies or styles to achieve their investment objectives. (p. 1) As the Reuters 3000 Xtra software uses the LGC throughout its system, this categorization will also be used in this paper and for the fund selection process. The first restriction that has been imposed is to only look at open-end funds and exclude all other fund types, such as closed-end funds, Real Estate Investment Trusts (REITs), or hedge funds from the sample. This has been done as closed-end funds restrict money in and outflow and, therefore, are not as popular as open-end funds, which (in regular market conditions) do not have these restrictions. As of February 13, 2009, there were 267,616 open-end funds registered in the Reuters 3000 Xtra system,1 while all other Copyright © 2010. Diplomica Verlag. All rights reserved.

fund types together accounted for 98,287 funds. Hedge funds and REITs, for example, show very different return distributions from regular mutual fund investments and therefore demand hedge fund or real estate specific performance measures that are not in the scope of this paper (Ackermann, McEnally, & Ravenscraft, 1999; Below & Stansell,

1

There are 365,903 funds registered in the Reuters 3000 Xtra system as of February 13, 2009. This number, however, includes multiple share classes and registrations of the same fund at different stock exchanges. Double counted funds are removed by use of the ISIN in a later stage of the selection process.

20

Fund Performance Measurement

2003). The second restriction puts a focus on funds that are registered for sale in Germany (GER), the United Kingdom (UK), and the United States (US). According to the Reuters 3000 Xtra system, these are the three single largest markets for investment funds with 56,919 (GER), 41,461 (UK) and 34,035 (US) registered open-end investment funds respectively. In the next step, the investment universe of the funds has been restricted to certain asset classes, styles and regions. As this study aims at analyzing and characterizing performance measures of certain distinct asset classes, balanced funds, which are funds consisting of equities, fixed income, and/or money market securities, have been completely excluded (Wolde, 1998). A complete overview of the fund types that are analyzed in this study can be seen in Table 1 and will be explained subsequently. Generally speaking, three distinct asset classes have been selected, which are expected to show very different risk and return characteristics. In the equity class, funds with a focus on one of the following equity markets have been selected: Europe, Germany, UK, or US. These are the major developed equity markets. An analysis of emerging or developing equity markets would be subject for further research, as these markets can be illiquid, and the data availability is rather difficult. Additionally, a distinction has been made between large cap funds, that are funds that invest in companies with a large market capitalization, and small cap funds, that are funds that invest in smaller companies as there are significant differences in terms of risk and return anticipated between these categories. Due to the limited number of small cap equity funds in the German sample, this category had to be eliminated. In the fixed-income class, corporate investment grade2 bond funds have been selected that focus on the currencies of British pounds (GBP), Euro (EUR), and United States dollar (USD). These are the three major currencies for corporate bond emissions according to the Reuters 3000 Xtra system. Finally, the same three major currencies (GBP, EUR, and USD) have been used to select relevant funds in the money market Copyright © 2010. Diplomica Verlag. All rights reserved.

class. After having retrieved and consolidated the funds list of the Reuters 3000 Xtra system, 28,925 funds had to be further analyzed. There were certain index-type funds left in the list that were removed in the first step. These passive funds are not in the scope of this

2

Investment grade corporate bonds show a rating of AAA to BBB- (Standard & Poor’s, Fitch) or Aaa to Baa3 (Moody’s).

21

Fund Performance Measurement

study, as only the performance of actively managed funds and their managers will be analyzed. As the Reuters 3000 Xtra system does not provide a sufficient history of return data for the funds, Thomson Financial DataStream has been used to perform the following steps. The launch date that is the first date of issue of a fund and its base currency have been retrieved via DataStream, and all funds have been removed that were generally not available via the DataStream system. Additionally, all funds with a launch date later than January 1, 2007, have been removed, as a minimum of two years of returns are required for a fund to be allowed into the dataset. This restriction assures that funds that are new to the market and still being established do not influence the results. Additionally, the launch date of each fund has been converted into a launch year, that is the first year in which a meaningful performance measure can be calculated for this specific fund. The launsch year is equal to the year in which a fund initially appeared in the market for at least 6 out of 12 months of a calendar year. This is done in order to reliably calculate the standard deviation that requires a sufficient amount of return observations. The final list of funds to be analyzed consists of 9,632 distinct funds for which weekly return index data from January 1, 1998 to December 31, 2008 have been retrieved via Thomson Financial DataStream. For funds quoted in a currency other than the corresponding benchmark currency, the return index data has been converted accordingly by incorporating the appropriate exchange rate. Additionally, daily and monthly return data in the given timeframe have been retrieved only for large cap US equity funds in order to analyze the influences of data frequency in Section 4.4. The return index data and static data3 for each fund have been jointly loaded into a MATLAB 7.7.0 data structure for further analyses. Table 1 provides an overview of the sample size of the dataset grouped by fund classifi-

Copyright © 2010. Diplomica Verlag. All rights reserved.

cations for selected years. The sample size in the years 2007 and 2008 is constant, as funds are required to have at least two years of return data before being included into the dataset. It can clearly be seen that the Equity US funds are the single largest category, followed by Equity Small Cap US funds. Therefore, after some general analyses with all fund categories, additional statistical tests and calculations will only focus on

3

The static data for each fund consists of name, ISIN, fund classification, domicile, currency, and base year.

22

Fund Performance Measurement

Equity US funds, as the large sample size has very favorable statistical properties and can deliver significant results compared to a sample of, for example, only 100 funds. It is worth noting that due to the introduction of the EUR currency, no Corporate Bond EUR or Money Market EUR funds were available prior to 2002. Table 1: Sample Size of the Fund Dataset Grouped by Fund Classification Fund Classification Equity Europe

1998

Number of Funds in the Dataset in Year… 2000 2002 2004 2005 2006 2007/08

127

214

363

553

689

813

895

54

57

65

70

73

80

84

Equity UK

189

267

370

514

570

658

681

Equity US

970

1,341

2,117

2,832

3,203

3,648

3,953

Equity Small Cap Europe

31

64

98

132

152

184

202

Equity Small Cap UK

51

67

83

109

111

127

132

Equity Small Cap US

529

775

1,237

1,653

1,842

2,057

2,184

Corporate Bonds EUR

0

0

49

129

151

171

185

Corporate Bonds GBP

50

86

124

167

187

211

222

Corporate Bonds USD

88

108

158

203

211

231

237

Money Market EUR

0

0

164

223

243

283

300

Money Market GBP

36

53

79

94

99

112

118

Money Market USD

202

230

320

396

410

433

439

Equity Germany

Source: Own aggregation based on Reuters 3000 Xtra and Thomson Financial DataStream

A special problem is created by the fact that the Reuters 3000 Xtra and Thomson Financial DataStream systems only list funds that are currently available for purchase on the market. Unsuccessful funds that ceased to exist are no longer listed. Therefore, a certain survivorship bias is present in the data, especially for the years before 2007, as only those funds that survived until today are contained in the dataset. It can be hypothesized Copyright © 2010. Diplomica Verlag. All rights reserved.

that the calculated performance measures of the empirical study might be too high when applied to unbiased data. The extent of and possible corrections for the survivorship bias will be analyzed in detail in Section 4.5. (Cranshaw, 1977, pp. 476-377)

23

Fund Performance Measurement

3.2

Benchmark Selection

The calculation of certain performance measures, such as the Information Ratio, requires a market benchmark against which the fund performance is compared. Usually every fund manager defines his benchmark in the fund prospectus and is also judged against it. However, in light of the large number of funds and a certain variety of benchmarks within the same fund category it was not possible to calculate the performance measure with the benchmark that is specified by each fund manager. Therefore, a general benchmark for each fund category has been used. Initially, this might seem inequitable, but on second thought, one might reason that it is fair to judge each fund within a certain investment universe against the same benchmark. Still, it is important to select an appropriate benchmark. The possible effects of selecting an appropriate or inappropriate benchmark will be further analyzed in Section 4.3 of the empirical analysis. Table 2 provides an overview of the benchmarks that have been assigned to the different fund classes.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Table 2: Overview of Benchmark Indices Fund Classification

Benchmark Name

DataStream Ticker

Equity Europe

MSCI Europe

MSEROP

Equity Germany

DAX

DAXINDX

Equity UK

FTSE 100

FTSE100

Equity US

S&P 500

S&PCOMP

Equity Small Cap Europe

MSCI Europe

MSEROP

Equity Small Cap UK

FTSE All Share

FTSEALLSH

Equity Small Cap US

S&P 600 Small Cap

S&P600I

Corporate Bonds EUR

iBoxx Liquid EUR Corporates

IBELCAL

Corporate Bonds GBP

iBoxx Liquid GBP Corporates

IB£CSAL

Corporate Bonds USD

Merrill Lynch Corporate Master

MLCORPM

Money Market EUR

EUR Interbank 3M Offered Rate

BBEUR3M

Money Market GBP

GBP Interbank 3M Offered Rate

BBGBP3M

Money Market USD

USD Interbank 3M Offered Rate

BBUSD3M

Source: Own aggregation, Thomson Financial DataStream

In the following, the benchmarks and their characteristics will be discussed in detail. The Morgan Stanley Capital International (MSCI) Europe Index is a free-float adjusted 24

Fund Performance Measurement

market capitalization weighted index for developed equity markets in Europe. It is, therefore, appropriate as a benchmark for funds with an investment universe covering European equities (MSCI Barra, 2009). The performance of German large cap equities is best reflected in the Deutsche Aktienindex (DAX), which covers the 30 largest German companies that are traded on the Frankfurt stock exchange. The DAX has been provided by Deutsche Börse AG since 1959 (Deutsche Börse AG, 2009, p. 8). The FTSE 100 index is a market capitalization weighted index of the 100 largest companies in the UK, covering approximately 82% of the total market capitalization in the UK. It has been provided by the FTSE Group since 1984 (FTSE International, 2009a, pp. 1-3). The Standard & Poor’s 500 index is widely regarded as the best gauge for the US equity market, covering 500 US large cap companies and approximately 75% of the total US market capitalization (Standard & Poor's, 2009a). The FTSE All Share index covers approximately 99% of the total market capitalization in the UK and has 619 constituents. It has been calculated since 1962 (FTSE International, 2009b). The Standard & Poor’s 600 Small Cap index is one of the best known small cap indices of the US, covering 600 companies and approximately 3% of the total US market capitalization (Standard & Poor's, 2009b). All three corporate bond indices had to be chosen mostly due to data availability. However, they still provide a good estimate of the bond markets of the respective currencies. The iBoxx Liquid indices are based on an aggregation of daily corporate bond transactions of several banks and are provided by the International Index Company Ltd. The Merrill Lynch Corporate Master index serves as a benchmark for the US corporate bond market. All three money market indices are the respective London Interbank Offered Rates (LIBOR) which are fixed by Thomson Reuters and published by the British Bankers’ As-

Copyright © 2010. Diplomica Verlag. All rights reserved.

sociation (BBA) every day around noon London time. These rates are widely regarded as an international benchmark for costs of borrowing in the money markets, and have been quoted since the early 1980s with the exception of the EUR rate, which was introduced in 1999 (British Bankers' Association, 2002; Cummings, 2008). As seen in Figure 2, the four different indices of US securities show characteristic, yet very different risk and return attributes. While the 3-months LIBOR USD rate has an extremely low volatility and limited returns, the S&P 600 Small Cap Index shows high 25

Fund Performance Measurement

volatility and return possibilities. These parameters are also generally reflected in the risk/return attributes of the respective fund categories. Being an excellent active fund manager, therefore, means generating returns superior to the benchmark with a lower standard deviation, that is optimally generating equity-like returns with a fixed-incomelike standard deviation. Figure 2: Index Development of Several Security Types 300 S&P 500 S&P 600 Small Cap 250

Merrill Lynch Corporate Bonds USD 3M Offered Rate

200

150

100

50 1-Jan-98

1-Jan-00

1-Jan-02

1-Jan-04

1-Jan-06

1-Jan-08

Source: Thomson Financial DataStream, indices rebased at 100 on January 1, 1998

3.3

Descriptive Statistics

Based on the return index data of all funds and benchmarks, continuously compounded weekly returns have been calculated for further analyses according to Equation 11: (11)

⎛ P ⎞ ri ,t = ln⎜⎜ i ,t ⎟⎟ ⎝ Pi ,t −1 ⎠

Copyright © 2010. Diplomica Verlag. All rights reserved.

where ri,t is the return of security i at time t, Pi,t is the price of security i at time t and Pi,t-1 is the price of security i at time t-1. Table 3 outlines the descriptive statistics of fund returns for each fund category during the observation period of January 1, 1998 through December 31, 2008, as well as the average annualized alpha over the respective benchmark. Returns and standard deviations are annualized for better comparability; the alpha has been calculated as annual return of the fund category above the respective benchmark.

26

Fund Performance Measurement

Table 3: Descriptive Statistics of Fund Returns Fund Classification

Avg. Ann.

Avg. Ann.

Return

Std. Dev.

Excess

Avg. Ann.

Kurtosis

Alpha

-0.72%

17.73%

-0.5394

2.8853

-1.71%

Equity Germany

0.18%

23.42%

-0.4183

3.4838

-0.60%

Equity UK

1.97%

15.30%

-0.7217

3.1672

0.68%

Equity US

-2.57%

18.23%

-1.0917

9.7343

-3.22%

Equity Small Cap Europe

1.51%

19.25%

-0.9861

2.8161

2.50%

Equity Small Cap UK

4.09%

14.02%

-1.2231

3.0204

2.27%

Equity Small Cap US

-2.54%

21.68%

-1.1508

9.1193

-6.45%

Corporate Bonds EUR

2.38%

2.88%

-0.6661

3.9141

-1.20%

Corporate Bonds GBP

3.65%

4.39%

-0.5720

2.6615

-1.12%

Corporate Bonds USD

3.10%

4.22%

-0.5507

1.7100

-1.58%

Money Market EUR

2.11%

0.30%

-3.5572

20.2996

-0.25%

Money Market GBP

4.97%

0.45%

4.1933

26.2449

0.72%

Money Market USD

1.97%

3.12%

1.3789

33.2211

-0.93%

Equity Europe

Skewness

Source: Own calculations, Thomson Financial DataStream

While money market and corporate bond funds behaved as expected in terms of risk/return behavior, the equity segment did not have consistent characteristics. It should be highlighted that the poor performance of equity securities within the 11-year period is mainly owed to the impact of the financial crisis on the global equity markets in 2008 and this fact should not suggest that equity investments are inferior per se. This is also supported when looking at Figure 2. Gains stemming from 2003 to 2007 in the US equity market were erased completely in 2008. In terms of manager performance, it can clearly be seen that on average, managers were not able to beat the benchmark in almost all asset classes and fund categories over an 11-year period. It is also worth noting that

Copyright © 2010. Diplomica Verlag. All rights reserved.

the money market segment shows strong leptokurtic returns. The effects of nonnormally distributed returns on performance measures will be further analyzed in Section 4.5 of the empirical analysis.

27

Fund Performance Measurement

4

Empirical Study on Selected Performance Measures

The empirical study is the main part of this thesis. Based on the theoretical concepts of performance measurement in Sections 2.1 and 2.2, the different characteristics and the reliability of selected measures will be tested by use of a large sample of fund data. Finally, all information gathered in the empirical analyses will be put together in a scheme that assists fund management companies in evaluating the performance of their managers.

4.1

Is the Information Ratio a Reliable Measure of Performance?

The Information Ratio is central to this study and will, therefore, be analyzed in full detail for all fund categories and for the whole observation period from January 1, 1998 through December 31, 2008. This part of the empirical study attempts to clarify several research questions. The first point to be analyzed is whether the distribution of Information Ratios is stable over time and across different fund categories. To answer this question, the Information Ratios for each year and for each asset class will be separated into four quartiles. A Wilcoxon signed-rank test and an optional student t-test will be used to assess the yearly values against an overall average for significant difference. Secondly, the categorization of Information Ratios according to Grinold & Kahn (2000, p. 114), Jacobs & Levy (1996, p. 12), and Goodwin (1998, p. 41) will be tested for validity, and, if necessary, an own classification will be introduced. Finally, graphical representations of the distribution of Information Ratios over time will be presented. All Information Ratios have been calculated in MATLAB according to Equation 7 as outlined in Section 2.2. The Information Ratios are presented in an annualized form for better readability and comparability. Annualization has been done similar to Method 1 in Goodwin (1998, p. 37) using arithmetic mean excess returns. However, for testing purposes, Information Ratios were also calculated based on Methods 2 through 4 in Copyright © 2010. Diplomica Verlag. All rights reserved.

Goodwin (1998, pp. 37-38) and not found to be significantly different. In order to correct for outliers, the best and worst 5% of the funds in terms of Information Ratio in each fund category and year were eliminated from the sample. This corrective measure has been empirically developed and found to deliver better results with the dataset at hand. It will be applied in all analyses within this study. The remaining sample has been divided into four quartiles, containing the first 25% (“very good”), the second 25% (“good”), the third 25% (“below average”) and the last 25% (“poor”) of the funds based 28

Fund Performance Measurement

on the Information Ratio. A finer categorization, for example using deciles, does not .

seem feasible as the value ranges of certain quantiles would be too narrow to be reliable. Table 4 presents the threshold values of the four quartiles, which are averages over the 11-year horizon of the dataset. This means, for example, that funds of the category “Equity Europe” with an Information Ratio above 0.40 are considered to be among the top 25% of all funds of this category. However, the threshold values vary considerably over time. While Table 4 provides an overview of the empirical results, detailed information about the threshold values and their development over time can be found in Appendix A, Table 12 and Table 13. Table 4: Information Ratios of Different Fund Categories IR 1st 25%

IR 2nd 25%

IR 3rd 25%

IR 4th 25%

“very good”

“good”

“below avg.”

“poor”

Equity Europe

> 0.40

0.40 to 0.04

0.03 to -0.36

< -0.36

Equity Germany

> 0.07

0.07 to -0.11

-0.12 to 0.37

< -0.37

Equity UK

> 0.32

0.32 to -0.01

-0.02 to -0.30

< -0.30

Equity US

> 0.28

0.28 to -0.40

-0.41 to -1.01

< -1.01

Equity Small Cap Europe

> 0.80

0.80 to 0.40

0.29 to -0.09

< -0.09

Equity Small Cap UK

> 0.59

0.59 to 0.22

0.21 to -0.12

< -0.12

Equity Small Cap US

> 0.08

0.08 to -0.60

-0.61 to -1.18

< -1.18

Corporate Bonds EUR

> -0.24

-0.24 to -0.76

-0.77 to -1.30

< -1.30

Corporate Bonds GBP

> 0.03

0.03 to -0.46

-0.47 to -0.95

< -0.95

Corporate Bonds USD

> 0.03

0.03 to -0.58

-0.59 to -1.29

< -1.29

Money Market EUR

> 4.30

4.30 to 1.36

1.35 to -0.39

< -0.39

Money Market GBP

> 4.30

4.30 to 0.31

0.30 to -1.50

< -1.50

Money Market USD

> 2.46

2.46 to 0.39

0.38 to -1.29

< -1.29

Fund Classification

Source: Own calculations

Copyright © 2010. Diplomica Verlag. All rights reserved.

It is worth noting that the Information Ratios show very different patterns for each fund category, not only in terms of values but also in terms of ranges. An Equity Europe fund can usually be classified “very good” with an Information Ratio of above 0.40, whereas a Money Market EUR fund with a similar Information Ratio would be “below average”. Additionally, the value range for a “good” Equity Europe fund is far narrower with Information Ratios between 0.40 and 0.04 compared to “good” Money Market EUR funds. Still, within the asset classes (Equity, Small Cap Equity, Corporate Bonds, and 29

Fund Performance Measurement

Money Market) the values and ranges seem to be similar with certain exceptions. While further testing has to be done to confirm these results, it becomes clear that general statements about the Information Ratio such as Grinold & Kahn (2000, p. 114) do not seem to be correct for all asset classes and in all calendar years. When looking at Appendix A, Table 12 and Table 13 it is striking that the Information Ratios of the same fund category vary more or less strongly over time. This leads to the question of whether the variations are statistically significant or not. In order to test for this difference, the median Information Ratio of the top 50% of all Equity US funds has been calculated for each of the 11 years. The median of the top 50% of the funds is equal to the threshold value between the first 25% and the second 25% of the funds. It is then tested to see if the threshold value in each year is significantly different from the average threshold value presented in Table 4. The results are outlined in Table 5 with the threshold values shown in the first data row and z-statistics shown in the second row. Values flagged with an asterisk are significantly different at the 5% significance level from the overall average value presented in the far right column according to the Wilcoxon signed-rank test. The Wilcoxon signed-rank test has been used as the Information Ratios are not normally distributed according to the Lilliefors test4 (for detailed test statistics see Appendix A, Table 14) and are assumed to be dependent on each other (Hollander & Wolfe, 1973, p. 27). Table 5: Test Statistics for the Difference of Threshold Values of Equity US Funds 1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

Avg.

-0.39*

0.36*

0.66*

0.51*

0.71*

0.36*

0.18*

0.55*

-0.38*

0.44*

0.08*

0.28

-16.5

-3.0

-15.4

-12.5

-19.8

-9.0

-3.2

-20.7

-34.3

-15.4

-4.0

---

Source: Own calculations * = value significantly different from average, alpha = 5%

Copyright © 2010. Diplomica Verlag. All rights reserved.

The results in Table 5 clearly show that the threshold values are significantly different from the 11-year average in every single year. A look at the z-statistics reveals that the values actually are far from being even close to the average value. This is also high-

4

The Lilliefors test is a generalization of the Kolmogorov-Smirnov test for normality. While the Kolmogorov-Smirnov test requires the specification of population mean and variance, the Lilliefors test is capable of testing samples with incompletely specified distribution characteristics for normality. (Lilliefors, 1967)

30

Fund Performance Measurement

lighted by the fact that the range from the lowest value of -0.39 in 1998 to the highest value of 0.71 in 2002 is so large that a certain fund could be categorized “below average” although it is actually “very good” when using the 11-year average value for classification as the only reference. To conclude, Information Ratios have to be calculated anew on a year-to-year basis in order to be reliable. In the next step similarity and dissimilarity of Information Ratios across different fund categories will be investigated. The focus will be on different US funds, as it seems more likely to find similar Information Ratios when looking at several asset classes within one country than across different countries. Again, the median Information Ratio of the top 50% of the funds of the respective category is calculated for the years 1998 and 2008. To reiterate, the median is equal to the threshold value separating the first 25% from the second 25% of the funds. The median value is then tested for significant difference from the average median value across the four fund categories by use of the Wilcoxon signed-rank test and results are presented in Table 6. Significantly different values at the 5% level are flagged with an asterisk (first and third data row); the second and fourth data rows show the respective z-statistics. Analog to the previous test, Information Ratios are not normally distributed according to the Lilliefors test (for detailed test statistics see Appendix A, Table 15). Table 6: Test Statistics for the Difference of Threshold Values of US Funds Year 1998

2008

Equity

Small Cap Equity

Fixed-Income

Money Market

Average

-0.39*

0.65*

-0.37*

1.80*

0.42

-17.53

-6.39

-5.51

-3.82

---

0.08*

-0.52*

0.71*

1.20*

0.37

-10.10

-26.66

-5.17

-4.04

---

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations * = value significantly different from average (level of significance = 5%)

Similar to the results presented in Table 5, Table 6 shows that all threshold values are significantly different from an average of these values. This statement is valid for the years 1998 as well as 2008, so it can be considered rather robust. Therefore, Information Ratios not only change over time but also between different fund categories. This is why general statements about fix threshold values like Grinold & Kahn (2000, p. 114) or Jacobs & Levy (1996, p. 12) cannot be confirmed. The results of this part of the em31

Fund Performance Measurement

pirical study are similar to the results of Goodwin (1998, pp. 39-41) with the addition that Information Ratios also change over time. Figure 3 uses box plot diagrams to graphically illustrate the different distributions of Information Ratios over time for Equity US and Equity Germany funds. The upper and lower edge of each box marks the 75th and 25th percentile, while the central line represents the median. Whiskers extend from the boxes to cover approximately 99% of all sample values. Outliers are symbolized by red plus signs. (McGill, Tukey, & Larsen, 1978, p. 12) Figure 3: Box Plots of Equity US and Equity Germany Fund Information Ratios

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations

Before concluding this section, one should not forget about investment constraints and their impact on the Information Ratio. Typical constraints can range from long only requirements and country restrictions up to detailed black lists that incorporate companies that are found to be unethical or not environmentally friendly. The so called Transfer Coefficient (TC) measures the correlation of the manager’s forecasts with the actually implemented portfolio. While a manager without any constraints will end up with a 32

Fund Performance Measurement

TC of 1, the constrained manager can only achieve a lower result. A usual long-only fund will possibly achieve a TC between 0.2 and 0.4, which significantly impacts the fund’s Information Ratio, as the manager is not able to fully transfer his skills into actual investment decisions. When assuming a (constrained) fund with a TC of 0.5, the manager has to double his skill (his IC) or quadruple the breadth in order to achieve the same Information Ratio as an unconstrained manager for an equal fund. (Wander, 2003)

4.2

The Information Ratio Versus Other Measures

After having thoroughly analyzed the Information Ratio in the previous section, it is now time to compare it against other measures. As outlined within the introduction and theoretical overview, the Information Ratio is in the center of interest of this study. However, the question has to be asked whether the Information Ratio is the single best measure for evaluating the performance of an active manager or whether there are other measures that are superior in certain cases. While various measures and ratios have been developed over time, only several of them could be discussed in Section 2.1 of this paper. Due to the limited scope of this thesis, only the two most important measures, namely the Sharpe Ration and Sortino Ratio, will be compared against the Information Ratio in this sub-section. An additional measure will be introduced at the end of this section, which corrects for certain shortcomings of the Information Ratio when being applied to funds with a negative alpha. Owing to the large dataset at hand, it is not possible to present the results for all fund categories and all years. The large sample size of Equity US funds is the reason for a focus on this category in the following analyses. Whenever possible, results for different years will be compared against each other to test for robustness. In the first step, Sharpe Ratios and Sortino Ratios have been calculated in MATLAB Copyright © 2010. Diplomica Verlag. All rights reserved.

based on Equations 2 and 4 respectively. As the computation of the Sharpe Ratio requires an assumption about the risk-free rate, the average annualized LIBOR rates over the 11-year period for EUR, GBP, and USD have been used. They are 2.30%, 4.25%, and 2.90% respectively. For funds investing in European or German Equities, as well as Corporate Bonds EUR and Money Market EUR instruments, the EUR LIBOR rate has been applied. For funds investing in US securities, the USD LIBOR rate has been used, while for funds investing in UK securities the GBP LIBOR rate has been applied. 33

Fund Performance Measurement

Secondly, the distribution properties of the different ratios have been calculated and can be found in Appendix A, Table 16 for the years 1998 and 2008. While the possible effects of the different distributions of the ratios will be considered further in section 4.5, at this point it should be noted that the three measures show very different distributions, and are, therefore, not easily comparable in terms of their values and ranges. The Information Ratio’s distribution is quite close to a normal distribution, but both other measures are not. Figure 4 charts the development of the threshold value between the first 25% and the second 25% of the Equity US funds in terms of Sharpe Ratio, Information Ratio, and Sortino Ratio. To clarify, funds with a performance measure above the respective line are among the first 25% of the funds (“very good”), and funds with a lower performance measure are among the second 25% of the funds or worse. The Sortino Ratio and Information Ratio for Equity US funds are moving similarly and are more stable compared to the Sharpe Ratio, which behaves very differently. This can partly be explained by the fact that the Sharpe Ratio uses returns above a constant risk-free rate in the numerator and absolute risk in the denominator. Both other ratios utilize relative returns and risks compared to a certain benchmark, which can possibly provide for smoother and more equal realizations over time. Detailed results of the Sharpe Ratio and Sortino Ratio for the different fund categories and years can be found in Appendix A, Table 17 to Table 20.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 4: Selected Performance Measures for Equity US Funds

Source: Own calculations

34

Fund Performance Measurement

In evaluating an active manager’s performance, it is not the absolute value of a certain performance measure that is relevant, but the relative ranking of the manager’s fund among other funds that are established by use of a certain ratio. This is the reason why funds have been categorized into performance quartiles (“very good”, “good”, “below average”, and “poor”) from the beginning of this paper, and threshold values have been calculated that illustrate the boundaries of these quartiles. The idea of creating rankings with certain performance measures also opens up the possibility of directly comparing the power of different measures despite the fact that they show different distribution characteristics. Figure 5 shows scatter plots of rankings using different performance measures. In all three plots, the same 970 Equity US funds that the dataset contains for the year 1998 have been ranked. The first ranking position (rank 1) always corresponds to the best fund; the last ranking position (rank 970) shows the worst fund. The dashed red line is the result of a linear regression of one ranking on the other ranking. Its slope is equal to Spearman’s rho, a well-known rank correlation coefficient. The first scatter plot in Figure 5 compares the ranking created by use of the Information Ratio with a ranking of the funds solely by their alpha. There are only minor differences in terms of ranking for the first 200 funds. However, the remaining funds highlight ranking differences, but these differences do not point into a distinct direction. A Spearman’s rho of 0.8619 points to a relatively close relationship between both performance measures. Interestingly, the simple alpha measure, which does not incorporate any gauge for risk, is not fundamentally wrong in terms of performance evaluation when compared to the more sophisticated Information Ratio. The second scatter plot analyzes the ranking relationship between the Sharpe Ratio and the Information Ratio. This relationship is characterized by a Spearman’s rho of 0.7920 and, therefore, it is not as close as in the previous case. Also the scatter plot reveals many ranking differences, which are crated mainly due to the fact that the Sharpe Ratio uses absolute returns and Copyright © 2010. Diplomica Verlag. All rights reserved.

risks while the Information Ratio employs relative returns and risks. Finally, the third scatter plot contrasts the ranking by Sortino Ratios with the ranking by Information Ratios. A close relationship can easily be recognized that is also characterized by a Spearman’s rho of 0.9809. Interestingly, the plot shows a stronger dispersion of data points above the red regression line. This is an indication for the punishment of downside volatility by the Sortino Ratio as described in the theoretical overview.

35

Fund Performance Measurement

Figure 5: Fund Rankings of Selected Performance Measures

Source: Own calculations

In order to formalize the ranking relationships described in the previous paragraph, besides Spearman’s rho additional measures of correlation are calculated: the Pearson correlation, Lin’s concordance, and Cohen’s kappa. This time, ranking relationships in two different years (1998 and 2008) have been tested in order to illustrate stability over time. While the Pearson correlation and Lin’s concordance are classified as parametric measures of association, Spearman’s rho and Cohen’s kappa belong to the category of non-parametric measures of association. The Pearson correlation is a well known paraCopyright © 2010. Diplomica Verlag. All rights reserved.

metric measure but especially for continuous data inferior to the concordance coefficient proposed by Lin (1989; 2000). With respect to the non-parametric dimension, Spearman’s rho and Cohen’s (1960) kappa are used. The kappa measure employs a contingency table-based approach to judge the agreement of different raters, which in this case are different performance measures. In order to be able to apply this measure, the median value for each performance measure has been calculated for the sample of 970 Equity US funds in 1998 and 3,953 Equity US funds in 2008. Funds that show a per36

Fund Performance Measurement

formance measure above the median are categorized winners, while all remaining funds are losers. Thereafter, the results based on the Information Ratio can be compared to the results based on each of the three other performance measures and four distinct categories are created: funds that are winners according to both measures, funds that are losers according to both measures, funds that are winners according to the Information Ratio but losers according to the other ratio, and funds that are losers according to the Information Ratio but winners according to the other ratio. The resulting matrix is then evaluated using Cohen’s kappa. This approach is based on Hübner (2007, p. 70). All results can be found in Appendix A, Table 21. It is striking that the Sortino Ratio is very closely related to the Information Ratio according to all four correlation measures and in both years that were analyzed. In 1998, according to Lin’s concordance and the Pearson correlation, the Sharpe Ratio is more closely related to the Information Ratio than the alpha, while Spearman’s rho and Cohen’s kappa show the opposite relationship. In 2008, however, it is striking that the Sharpe Ratio is the performance measure that has the lowest correlation with the Information Ratio according to all four correlation coefficients. Two factors possibly contribute to this result: a larger sample size and the effects of the financial crisis on funds and benchmark returns in 2008. The Information Ratio, however, has a severe drawback when applied to funds with negative alphas. As this inconsistency affects the ability of the Information Ratio to correctly rank these funds according to their risk/return characteristics, it is important to further discuss this problem. Table 7 provides a simple example that illustrates this inconsistency. Fund A has an annual alpha of -6.96% with a tracking error of 13.86, which results in an Information Ratio of -0.50. Fund B, however, has a higher alpha of -3.62% and a lower tracking error of 5.03 compared to Fund A but still shows a lower Information Ratio. According to the Information Ratio, Fund A is better than Fund B. It is clear, however, that Fund B first-order statistically dominates Fund A in terms of risk Copyright © 2010. Diplomica Verlag. All rights reserved.

and return. (Israelsen, 2005) Table 7: Inconsistency of the Information Ratio for Negative Alphas Alpha

Tracking Error

Information Ratio

Fund A

-6.96%

13.86

-0.50

Fund B

-3.62%

5.03

-0.72

Source: Adapted from Israelsen (2005, p. 424)

37

Fund Performance Measurement

As this study has shown (cf. Table 3), on average active funds are not able to beat the benchmark. This means that there are a significant number of funds that show negative Information Ratios but still have to be categorized and ranked correctly for performance measurement. The whole problem intensifies in bear markets when even more funds show negative alphas. In order to deal with this issue, Israelsen (2005) developed the modified Information Ratio (mIR), which is shown in Equation 12: (12)

ER

mIR = TE

ER abs ( ER )

where ER is the annual excess return, TR is the annual tracking error and abs(ER) is the absolute value of the annual excess return. It is obvious that the modified Information Ratio only differs from the regular Information Ratio in case of negative excess returns. Figure 6 shows the divergence in rankings between the regular Information Ratio and the modified Information Ratio of 970 Equity US funds in the year 1998 by use of a scatter plot. As explained, both measures are equal for funds with positive alphas but differ largely for all other funds. Spearman’s rho is 0.7125, which is quite low compared to previous ranking relationships. All four correlation coefficients for the association between the Information Ratio and the modified Information Ratio can be found in Appendix A, Table 21. It can be concluded that the regular Information Ratio makes many mistakes when ranking funds with negative alphas by both underestimating and overestimating risk/return characteristics in different cases.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 6: Fund Rankings Using Modified Information Ratios

Source: Own calculations

38

Fund Performance Measurement

Figure 7 separates both input factors of the Information Ratio, the excess return and the tracking error, and plots both values based on the ranking of the regular and the modified measure. The method of illustration has been adapted from Israelsen (2005, p. 426) and applied to all Equity US funds with negative alphas in the year 1998 that are contained in the dataset. The upper chart clearly shows that the regular Information Ratio is not able to correctly order the funds in terms of their relative risk/return characteristics. The order is rather chaotic and meaningless. The modified Information Ratio, however, shows a different picture which is reflected in the lower chart. Funds are correctly ranked with a lower rank pointing to a more favorable risk/return profile of the respective fund. These are important results that have to be kept in mind in order to correctly judge the performance of all managers.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 7: Factor Decomposition of Rankings Based on Information Ratios

Source: Own calculations, method of illustration adapted from Israelsen (2005, p. 426)

A similar inconsistency for negative returns exists with the Sharpe Ratio and has been widely discussed in literature (Akeda, 2003; Israelsen, 2003, 2005; Jobson & Korkie, 1981). While Sharpe (1975; 1998) is of the opinion that his ratio is valid for all types of risk/return profiles and in all market conditions, several researchers (Israelsen, 2003, 2005; Scholz, 2006; Scholz & Wilkens, 2006) have developed extensions to the Sharpe 39

Fund Performance Measurement

Ratio in order to correct this anomaly. Although, due to the limited scope of this paper, this effect cannot be analyzed further, it should be kept in mind when working with the Sharpe Ratio to evaluate an active manager’s performance.

4.3

The Art of Selecting the Benchmark

The selection and allocation of benchmarks for this study (cf. Table 2), which are used to calculate the Information Ratios, has mostly been done based on popularity of the indices and their ability to cover the price development of a certain market. In fund management companies, the selection of a benchmark usually is the result of intense negotiations between the fund manager and the investors, as the benchmark has a major impact on the alpha of the fund and on the influences of specific investment restrictions. Depending on style and country focus, one benchmark might be more favorable to the fund manager than another. (Goodwin, 1998, p. 40; Grinold & Kahn, 2000, pp. 88-90) Therefore, it is necessary and important to analyze the sensitivity of the Information Ratio toward the selected benchmark within this paper. Lehmann & Modest (1987) have shown that benchmark selection does have a very strong influence on the resulting alphas as well as their volatility. While the Standard & Poor’s 500 Index has been used throughout this paper in connection with Equity US funds, two additional indices, the equally-weighted Dow Jones Industrial Average and the market-weighted Russell 1000 Index, will be introduced to compare the resulting Information Ratios. The Dow Jones Industrial Average is based on a basket of 30 large cap, industrial companies in the US. It has been quoted since 1896 and has a strong focus on manufacturers of industrial and consumer goods (Dow Jones Indexes, 2009). The Russell 1000 Index is a proxy for the large cap segment of the US equity market and is based on the 1,000 largest companies in terms of market value. The Russell 1000 covers about 92% of the US equity market, Copyright © 2010. Diplomica Verlag. All rights reserved.

has been calculated since 1984, and is in direct competition with the S&P 500 (Russell Investment Group, 2009). Figure 8 illustrates the development of the three indices over the 11-year observation period. It can be seen that the indices move very similarly. However, all of them emphasize different market segments and show a different behavior in certain periods.

40

Fund Performance Measurement

Figure 8: Development of Major Large Cap US Equity Indices 200 S&P 500 Dow Jones Industrial Average Russell 1000 150

100

50 1-Jan-98

1-Jan-00

1-Jan-02

1-Jan-04

1-Jan-06

1-Jan-08

Source: Thomson Financial DataStream, indices rebased at 100 on January 1, 1998

After having calculated three different Information Ratios (based on the S&P 500, the Dow Jones Industrial Average, and the Russell 1000) for all Equity US funds from 1998 to 2008, the threshold values between the first 25% of the funds and the second 25% of the funds have been calculated again. This threshold value separates the first quartile and the second quartile, that is “very good” funds from “good” to “poor” funds. The result is charted in Figure 9.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 9: The Effect of Benchmark Selection on the Information Ratio

Source: Own calculations

It can be recognized that the Information Ratios based on the S&P 500 and the Russell 1000 are closely related, while the Information Ratios based on the Dow Jones Industrial Average behave differently and are far more volatile. It seems that the Dow Jones 41

Fund Performance Measurement

Industrial Average does not cover the investment universe of the Equity US funds very well. This can be due to the fact that this index is only based on 30 companies. Differences that seemed to be little at first glance in Figure 8 had a major impact on the threshold values of the Information Ratios as presented in Figure 9. The difference of the threshold values has been tested for significance using the Wilcoxon signed-rank test. This test has been used, because all three sets of Information Ratios are not normally distributed according to the Lilliefors test and are assumed to be dependent on each other. The z-values of the Wilcoxon test are presented in Table 8, and significantly different values are flagged with an asterisk. Firstly, the Information Ratios based on the Dow Jones Industrial Average index were tested against those based on the S&P 500 index. Secondly, the Information Ratios based on the Russell 1000 index were also tested against those based on the S&P 500 index. To conclude, while some threshold values are quite close, all are significantly different from those based on the S&P 500 using a 5% level of significance. These results are in line with Goodwin (1998, pp. 40-42), who also found that the selection of the benchmark has a strong influence on the resulting Information Ratios. Table 8: z-Statistics for Significant Difference of the Information Ratios z-values for…

1998

1999

2000

2001

2002

2003

-18.1*

-9.6*

-9.3*

-22.0*

-26.6*

-26.4*

Russell 1000

-9.4*

-4.2*

-3.5*

-14.2*

-8.5*

-17.1*

z-values for…

2004

2005

2006

2007

2008

Dow Jones

-30.9*

-32.9*

-7.5*

-8.6*

-25.3*

Russell 1000

-25.0*

-12.7*

-31.9*

-21.1*

-33.5*

Dow Jones

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations * = value significantly different from S&P 500 Information Ratio, alpha = 5%

The results are confirmed when looking at the rankings based on the three different Information Ratios as illustrated in both scatter plots of Figure 10. While there are noticeable differences between Information Ratios based on the Dow Jones Industrial Average and those based on the S&P 500, the changes in rankings when using the Russell 1000 versus the S&P 500 are quite small. The selection of an appropriate benchmark is, therefore, an important step during performance analyses in general. Still, the results 42

Fund Performance Measurement

can only provide very limited guidance as to how to select the right benchmark. One can, however, conclude that benchmark indices that cover a large part of the investment universe of the specific fund category (for example, the Russell 1000 or S&P 500) are superior to indices that are only based on a few securities and certain industry sectors (for example, the Dow Jones Industrial Average). It should also be noted that the Dow Jones Industrial Average has been criticized for its equal weighting of stocks, lack of revision of its constituents following changes in the market environment, and a missing framework that describes admission criteria (Benders, 2009). The final decision for or against a benchmark should always be based on the experience of the performance evaluator. Figure 10: Ranking Differences Caused by Different Benchmarks

Source: Own calculations

4.4

Does Data Frequency Matter?

Usually, the selection of the appropriate data frequency, that is daily, weekly, monthly, etc., is at the researcher’s discretion. However, among others Ané and Labidi (2004) Copyright © 2010. Diplomica Verlag. All rights reserved.

have shown that the return interval has a significant impact on the distribution parameters of the data. While monthly and quarterly return data come close to a normal distribution, weekly and especially daily data usually shows strong leptokurtic characteristics. Furthermore, the annualized standard deviation varies with the data frequency (Ané & Labidi, 2004, p. 288). Additionally, other research has shown that the data frequency influences correlations and volatility, as well as the distribution parameters (Handa, Kothari, & Wasley, 1989). The question is, therefore, whether the data frequency also 43

Fund Performance Measurement

impacts the Information Ratio, in particular the threshold values that separate the quartiles. If there is any significant influence of the data frequency, it is the goal of this research to describe these differences and to provide guidance for selecting the appropriate return interval. In the first step, in order to highlight that there are differences, the distribution of S&P 500 returns has been briefly analyzed with daily, weekly, and monthly data over an 11-year horizon (January 1, 1998 through December 31, 2008). The results are presented in Appendix A, Table 22 and confirm the findings of the previously mentioned literature. The mean and standard deviation have been annualized5 for better comparability. It can be seen that the standard deviation decreases with decreasing data frequency. If the daily standard deviation is assumed to be the true standard deviation, which reflects all risks inherent in this market index, then the usage of monthly returns leads to an underestimation of the risk. Although the kurtosis for weekly data is the highest, which is quite unexpected, it can be seen that for low frequency (monthly) data the kurtosis is also very low. In the next step, annual Information Ratios have been calculated for Equity US funds using daily, weekly, and monthly fund returns. Appendix A, Figure 15 shows exemplarily the distribution of the Information Ratios in year 1999 for all three data frequencies. Extreme outliers with Information Ratios below -4 or above 4 are not shown in the histograms. It can be seen that the lower the frequency of the data, the more leptokurtic and non-normal is the distribution of the Information Ratios. This can be attributed to the fact that a large amount of information gets lost when switching from daily to monthly data. Using the ranking methodology explained in Section 4.2, fund rankings based on the three different Information Ratios have been created for the year 1999 and depicted in

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 11. While the rankings of Information Ratios based on daily and weekly data do not differ significantly, a switch from weekly to monthly data completely changes the picture – the ranking differences are enormous. It can be concluded that while there is no significant difference between the usage of daily and weekly data, a monthly fre-

5

Monthly data has been annualized with the assumption of 12 months per year; weekly data has been annualized with the assumption of 52 weeks per year; and daily data has been annualized with the assumption of 250 trading days per year.

44

Fund Performance Measurement

quency is inappropriate to calculate reliable performance measures. One has also to keep in mind that monthly data only allows for 12 data points per year, which cannot be considered enough to estimate a meaningful standard deviation. Usually, a sample of 20 observations or more provides a reliable estimate of the variance or standard deviation (D'Agostino, 1970; Padgette, 1995, p. 174). Figure 11: Comparison of Rankings Based on Different Data Frequencies

Source: Own calculations

4.5

Other Influences on Performance Measures

The quality and reliability of performance measures, especially the Information Ratio, can be influenced by several factors. As discussed in the previous sections, benchmark selection and data frequency are two of these factors. There are, however, two other important factors to be discussed: the distribution characteristics of the returns and a potential survivorship bias in the sample, which is used to calculate the threshold values between the quartiles. These factors will be discussed in the following.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Although literature has shown that returns do not generally follow a normal distribution, many popular performance measures are based on the mean-variance framework developed by Markowitz (1952), which assumes asset returns to be normally distributed. This particularly affects the Sharpe Ratio, the Treynor Ratio, the Information Ratio, and the Sortino Ratio as all of these measures are based on a risk/return analysis in terms of the mean-variance framework of Markowitz (1952). Non-normal returns can, therefore, lead to biased or even wrong results for these ratios (Benson, Gray, Kalotay, & Qiu, 2008, pp. 447-448). According to Stutzer (2000), non-normal returns can be caused by 45

Fund Performance Measurement

“large asymmetrical economic shocks, investments in options and other derivative securities with inherently asymmetrical returns, limited liability (bankruptcy) effects on asset returns, or other causes” (p. 52). Additionally, Kraus & Litzenberger (1976) found that positively skewed returns are actually favorable for investors as positive skewness decreases the probability of lower returns. None of the popular performance measures incorporates this property. It should also be added that the comparison of Sharpe Ratios that are based on returns with different distributions may be difficult and eventually misleading (Mahdavi, 2004, p. 47). In order to compensate for the above mentioned effects, improved performance measures have been developed. Mahdavi (2004) proposed the Adjusted Sharpe Ratio, which adjusts the original Sharpe Ratio so that it is comparable to Sharpe Ratios that are based on different return distributions. This is done with an option based approach. Stutzer (2000) developed the Portfolio Performance Index, which is independent of return distributions and also incorporates the preference of positive skewness. While the analysis of these measures with the dataset at hand goes beyond the scope of this paper, some conclusions with respect to nonnormality can be drawn based on the results that have been derived so far. Referring to Table 3, which presents descriptive statistics of fund returns for each category, it is striking that money market funds in all currencies seem to produce strongly skewed and leptokurtic returns. Keeping this information in mind, it can be understood, why the respective Sharpe Ratios, Information Ratios, and Sortino Ratios for these funds show odd and unexpected results. When comparing the threshold values of these three ratios that separate the first and second quartile to all other fund categories, the values for money market funds are inconsistently high. Therefore, it can be concluded that due to the special return distribution characteristics of money market funds, the common performance measures are not usable in this fund category. While all other fund categories also show non-normal returns, the lower extent of non-normality does not lead to inconCopyright © 2010. Diplomica Verlag. All rights reserved.

sistent or unusually high ratios. As already introduced in Section 3.1, this dataset is, to a certain extent, subject to a survivorship bias. This is due to the fact that all common data providers only list funds that are currently available on the market. Poor performing funds disappear over time as investors withdraw money, and will then usually be merged into other funds. Therefore, it can be expected that the estimated performance measures within this study are too high (Cranshaw, 1977, pp. 476-477). The interesting question, however, is whether this 46

Fund Performance Measurement

effect can be quantified. For many years the effect has been analyzed within the literature (Elton, Gruber, & Blake, 1996). Brown, Goetzmann, Ibbotson, & Ross (1992) found that the survivorship bias can be so strong that it erroneously leads to the conclusion that the performance of mutual funds is predictable. This finding disappears when the sample is corrected for survivorship bias. In terms of quantification of the survivorship bias for Equity US funds, Grinblatt & Titman (1989b) found a bias of 0.1% to 0.3% per year, Brown, Goetzmann, & Ross (1995) estimated the bias to be between 0.2% and 0.8% per year, and Elton et al. (1996) presented an average bias of 0.71% to 0.77% annually. In order to get an impression of the extent of the survivorship bias inherent in the dataset of this study, the following analysis has been performed. Information Ratios for the years 2007 and 2008 have been calculated for two different groups of funds. The first group consists of Equity US funds with a launch year of 1998 or before; the second group also consists of Equity US funds but with a launch year of 2005 or later. Outliers have been eliminated, and the Information Ratios have been put into four quartiles. Table 9 presents the threshold values separating first and second quartile funds, that is funds with an Information Ratio above the mentioned value are in the first quartile (“very good”). While minor differences were expected, the extent of the discrepancy in Information Ratios for older versus newer funds is consistently striking in both years. However, it has to be highlighted that this difference can be caused by many effects and survivorship bias could be one of them. It could also be that in general the newer funds show a very different risk/return profile when compared to the older funds. Therefore, no conclusion regarding any kind of corrective factor for survivorship bias should be drawn from these results.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Table 9: Information Ratios in Relation to Fund Launch Years Launch Year

Number of Funds

Information Ratio 2007

Information Ratio 2008

= 2005

1121

0.0792

0.0562

Source: Own calculations

47

Fund Performance Measurement

4.6

Performance Persistence: Outperformance by Luck or Skill?

After analyzing several performance measures and factors that influence these measures, the question has to be raised as to whether a single ratio based on one year of mutual fund returns is the only dimension to be used in order to evaluate a manager’s performance. Maybe it was just luck that the manager achieved a very good Information Ratio in a certain year. How can lucky portfolio managers be separated from skilled ones? The manager’s track record can be an adequate tool, as the probability for good performance by skill increases when the manager is able to position his fund among the top 25% two or even three years in a row (Bollen & Busse, 2005, p. 569). However, due care should be used when trying to predict future returns of a fund based on its past returns. Horst & Verbeek (2000) were, for example, able to show that previous studies, which claimed the existence of performance persistence, are subject to spurious and biased results. Kahn & Rudd (1995) and Carhart (1997) also analyzed the persistence of equity mutual funds and did not find a significant relationship between past and future performance. These findings can be proven based on the dataset at hand. Equity US funds with a launch year of 1998 or before have been categorized into four quartiles based on their 1998 Information Ratio, and the initial categorization has not been changed over the 11-year observation period. The average Information Ratios for each quartile has been calculated for 1998 and each subsequent year and is charted in Figure 12. It can be seen that the top quartile funds of 1998 actually have the lowest average Information Ratio after two years’ time. The chart creates the image of a mean reverting

Copyright © 2010. Diplomica Verlag. All rights reserved.

process. Obviously, good performance on average does not persist over time.

48

Fund Performance Measurement

Figure 12: Performance Persistence of Equity US Funds

Source: Own calculations

Based on the fact that good performance on average does not persist, it can be concluded that lucky managers without skill will not be able to stay among the best funds for multiple years in a row. A second dimension, the track record, is, therefore, proposed when evaluating the performance of fund managers. In order to visualize the luck versus skill effect, the performance of funds from selected categories with a launch year of 1998 or before that survived until 2008 has been tracked over the entire 11-year period. Every fund has been calculated as to the number of years it was among the top 25% of all funds6 within this 11-year period. Summarized results are presented in Table 10 and are as expected. It can be seen that 95.5% of all Equity US funds and 93.4% of all Equity Small Cap US funds are at least once among the top 25% of the funds during the 11-year period. Hence, if a fund survives an 11-year period, it is very likely that it will be in the top quartile in some years – just by luck. It should be noted that these results could partly be caused by changes in the fund management. Due to limited data availability, it was not possible to correct the sample for changes in the

Copyright © 2010. Diplomica Verlag. All rights reserved.

fund management.

6

Using the Information Ratio as ranking criterion

49

Fund Performance Measurement

Table 10: Number of Top 25% Ranks over Lifetime Fund Classification

0

1

2

3

4

5

6 or more

Equity US

4.5%

12.8%

21.4%

24.9%

17.7%

12.4%

6.3%

Equity Small Cap US

6.6%

11.0%

21.7%

24.4%

18.3%

9.3%

8.7%

Source: Own calculations

Taking the results presented in Table 10 one step further, it has been calculated how many funds are able to stay within the top quartile for two or three years in a row within a three-year period based on their Information Ratio. Funds that are able to stay among the top 25% of all funds of their category for three years in a row can be considered extraordinary according to Table 11, as on average only 2.76% of all funds manage to achieve such a result. The percentage of all funds that are able to stay within the top quartile two or three years in a row has been calculated for rolling three-year periods, and the results are fairly stable and consistent. Table 11 has to be interpreted as follows. When looking at the first row for the timeframe between 2008 and 2006, 0.93% of all Equity US funds were able to stay among the top 25% of the funds in all three years. 2.33% of all Equity US funds were able to stay among the top 25% in the years 2008 and 2007, and 21.73% were among the top 25% only in year 2008. These three values add up to 25% with only minor rounding differences. The number of funds that are ranked “very good” three years in a row should be and, in fact, are in almost all cases, lower than the number that only achieved the top ranking two years in a row. Additionally, the same calculation was performed using the top 50%, that is above the median. These results are quite inconsistent, and it can be concluded that the top 50% requirement can be achieved too easily and is, therefore, not an appropriate measure. As all of these results are considered to be quite interesting, Appendix A, Table 23 and Table 24 show the percentages for all fund classes except money market funds.7 Based on these Copyright © 2010. Diplomica Verlag. All rights reserved.

results, performance persistence (the track record of a manager) is another important factor of performance measurement in the separation of luck from skill. Therefore, it should be searched for a consistent series of top-ranked performance measures, in contrast to unrelated occurrences of good performance over a longer timeframe.

7

Money market funds have been excluded, as the analyses in Section 4.5 revealed that the Information Ratio is not an appropriate performance measure for this fund category anyway.

50

Fund Performance Measurement

Table 11: Performance Persistence of Equity US Funds Over Time Period

TOP 25% … years in a row

TOP 50% … years in a row

1 Year

2 Years

3 Years

1 Year

2 Years

3 Years

2008 to 2006

21.73%

2.33%

0.93%

25.73%

11.58%

12.67%

2007 to 2005

20.41%

2.88%

1.72%

28.22%

7.81%

13.94%

2006 to 2004

18.77%

3.04%

3.18%

26.48%

5.51%

17.99%

2005 to 2003

16.76%

4.07%

4.15%

20.87%

9.32%

19.81%

2004 to 2002

14.80%

7.57%

2.65%

18.20%

14.23%

17.54%

2003 to 2001

19.76%

2.33%

2.87%

25.49%

6.51%

17.97%

2002 to 2000

12.10%

5.15%

7.77%

13.22%

6.87%

29.87%

2001 to 1999

11.11%

13.17%

0.72%

10.66%

29.66%

9.68%

2000 to 1998

23.35%

0.83%

0.83%

34.09%

5.79%

10.12%

Mean

17.64%

4.60%

2.76%

22.55%

10.81%

16.62%

Source: Own calculations

4.7

Summary of Empirical Results

This section summarizes all results of the empirical analysis and exemplarily presents a framework for the performance evaluation of mutual funds in 2008. Overall, the analysis revealed that there are two dimensions that are important in order to judge the performance of a manager in a particular year: the performance measure that has been calculated for the fund in that particular year and the track record of the fund over the last three years. By using these two dimensions as a basis, a fair and structured ranking will be established. The performance of the fund in the year to be evaluated will be the basis, which is further adjusted upward or downward by examining the track record. Before visualizing this concept further, a summary of the most important findings is given in

Copyright © 2010. Diplomica Verlag. All rights reserved.

the following paragraph. The empirical study shows that Information Ratios are reliable measures of fund performance that are, however, subject to certain factors that can influence the quality and reliability of the measure. In order to transform an Information Ratio into a system that is similar to school grades, the categorization in quartiles has been introduced. By comparing the fund’s Information Ratio with the peer group’s ratios, a conclusion can be drawn about the quality of the fund. If the Information Ratio is among the top 25% of the peer group’s Information Ratios, the fund can be considered “very good”. A fund 51

Fund Performance Measurement

with an Information Ratio in the range of the second quartile is rated “good” and still among the top 50%, which means above average. Funds that show an Information Ratio in the range of the third quartile are classified as “below average”, and all remaining funds are rated “poor”. In order to operationalize this quartile-based system, threshold values are calculated that define the border between two quartiles. It has been proven that Information Ratios vary over time and also across different fund categories (cf. Table 5 and Table 6), so that it is necessary to calculate the threshold values anew for every calendar year. When looking at the power of other performance measures, the Sharpe Ratio has not been found to be reliable and stable over time as it is based on absolute return and risk measures (cf. Figure 4 and Figure 5). Generally, the Information Ratio is preferred over the Sortino Ratio because it is easier to handle, well known in the industry and always available.8 The Sortino Ratio is, however, recommended in order to distinguish two funds with a similar Information Ratio. A severe drawback of the Information Ratio has been found for all funds with negative alphas. In these cases, the ranking becomes inconsistent (cf. Table 7). In order to rank and evaluate funds with negative alpha correctly, the modified Information Ratio according to Israelsen (2005) has been introduced and tested. While the ratio seemed useful based on the dataset of this study, Scholz (2006, p. 351) demonstrated that this ratio improved the ranking quality but still had certain other drawbacks. Four factors influence the quality of the Information Ratio and the Sortino Ratio: benchmark selection, data frequency, non-normality of fund returns, and survivorship bias inherent in the sample that is used to estimate the threshold values. With respect to the benchmark, it is recommended to select an index that covers a large part of the respective market. Additionally, it is useful to compare Information Ratios based on different benchmarks for a certain market to check for robustness of the results. The data frequency for fund and benchmark returns should be rather high, that is daily or weekly Copyright © 2010. Diplomica Verlag. All rights reserved.

in order not to lose information about the standard deviation of returns (cf. Figure 11). Returns should also be tested for non-normality, as this influences the quality of the performance measures greatly. While all fund categories showed non-normal returns,

8

The Sortino Ratio cannot be calculated for funds that consistently outperformed the benchmark at all times (the denominator would be equal to zero) and it becomes unreliable if there are less than 20 observations of downside risk (tracking error) left to calculate the standard deviation due to a good performance.

52

Fund Performance Measurement

the extent of this property varied greatly across different categories. Only money market funds showed very strong non-normality and, consequently, the Information Ratio cannot be recommended for this type of fund. Still, the comparison, not only of Sharpe Ratios, but also of Information Ratios and Sortino Ratios, based on returns with different distribution characteristics should be done with due care, as the results can be biased or even wrong. A quantification of the survivorship bias within the Information Ratio is difficult and still unclear and, therefore, left open to further research. It should be noted, that the proposed framework is only valid for funds with symmetric return profiles. This means that funds with a downside protection by use of derivatives or similar strategies cannot be evaluated with the Information Ratio in general, as their returns are not normally distributed. A similar restriction applies to the Sharpe Ratio. According to Pedersen & Satchell (2002), the Sortino Ratio has a better predictive power in the case of asymmetric return profiles, but generally a measure that takes into account all higher moments of the return distribution, for example the Omega Measure (cf. Chapter 2.1.7), is recommended. It should additionally be kept in mind that funds investing in multiple asset classes are also very difficult to evaluate with the Information Ratio as explained in Chapter 2.2. Balanced funds were, therefore, excluded from this empirical study. The practical implications of these restrictions will be explained in Chapter 5 based on the results of several questionnaires. Figure 13 is an example of a performance evaluation framework based on the Information Ratios that have been calculated using the dataset of the empirical study. It is valid for funds of the selected categories in 2008 and helps to estimate the first performance dimension, the performance within the particular year to be evaluated. No differentiation has been made between funds belonging to the third or fourth quartile, that is “below average” or “poor” funds, as their Information Ratios are mostly negative and,

Copyright © 2010. Diplomica Verlag. All rights reserved.

therefore, unreliable.

53

Fund Performance Measurement

Figure 13: Framework for Performance Evaluation – Year 2008 -1.0

-0.5

0.0

0.5

1.0

1.5

Equity Europe Equity Germany Equity UK Equity US Corporate Bonds GBP Corporate Bonds USD „below average“ and „poor“

„good“

„very good“

Source: Own illustration based on Information Ratios as shown in Appendix A, Table 12 and Table 13

Funds with similar Information Ratios can be further separated in terms of their performance by use of the Sortino Ratio. Additionally, based on the findings of Section 2.4, it is recommended to calculate the Active Share measure for each fund according to Equation 10 in order to uncover closet indexers. Fund managers with low active shares should be penalized. Unfortunately, due to insufficient data availability, the Active Share measure could not be calculated and evaluated in this empirical analysis. Therefore, no suggestions can be provided as to which levels of Active Shares are to be considered “good” or “very good”. However, a qualitative split is provided in Figure 14. This also illustrates that the Active Share measure can only supplement the Information Ratio or Tracking Error. It also shows that a high Tracking Error is not negative per se.

Diversified Stock Picks

Concentrated Stock Picks

Closet Indexing

Factor Bets

Active Share

Copyright © 2010. Diplomica Verlag. All rights reserved.

Figure 14: Active Share Versus Tracking Error

Pure Indexing Tracking Error

Source: Adapted from Cremers & Petajisto (2007, p. 48)

54

Fund Performance Measurement

As a second dimension, the track record of the funds should also be considered to rate the fund performance. Based on the results presented in Appendix A, Table 23, and Table 24, a fund that was able to stay among the top 25% of the funds of its category two years in a row should be rated “very good” in the persistence dimension. A fund that was able to stay among the top 25% of the funds three years in a row is considered to be “extraordinary”. Both dimensions can be combined and transferred into a payment scheme if necessary.

5

A Practical View on Performance Measurement

This section is intended to complement the empirical results of the previous chapter from the perspective of different practitioners in order to highlight requirements and restrictions of day-to-day fund management. The main findings are based on several questionnaires that were completed by fund managers and by the head of performance evaluation of a large fund management company based in Frankfurt am Main, Germany. All completed questionnaires are reproduced in their original German language in Appendix B of this paper. In general, many empirical findings are confirmed by the practitioner’s views and experiences. However, there are also some important differences that will be highlighted. Firstly, the view of portfolio managers will be analyzed. The following results are based on the first four questionnaires found in Appendix B. All four fund managers have between 9 and 20 years of work experience and manage or oversee a large number of funds for investors, ranging from banks and insurance companies to non-profit organizations. While the performance measurement internally (within the fund management company) is rather sophisticated with different measures that incorporate excess returns and volatilities, it seems that the investing client is mostly focused on excess returns Copyright © 2010. Diplomica Verlag. All rights reserved.

above the benchmark or absolute returns. Interestingly, Mr. R. points out that most of the investors are not taking into account risk measures, for example the tracking error, when evaluating the fund performance. This is an important result, especially from an agency theoretic point of view (cf. Chapter 2.4). Academia and fund administrations developed and work with quite sophisticated performance measures that have been studied extensively, while investors – the group that should actually care the most – use rather simple methods for performance evaluation. This is in contrast to Grinold & 55

Fund Performance Measurement

Kahn (2000, p. 478) who stated that investors always were a driving force in the development of new performance measures. Unfortunately, a differentiation in this aspect between different investor groups is not possible based on these results. As anticipated, the selection and composition of benchmarks is far more sophisticated in practice than the methodology used in this study. While this study only analyzes funds with symmetric return distributions and with one single asset class as an investment universe, in practice, balanced funds and funds with protection levels are very common. It goes without saying that these funds require special benchmarks, which are created by combining several market indices. Additional option-based strategies within these benchmarks or money market rates plus an additional spread are used to replicate protection levels. Constant proportion portfolio insurance (CPPI) benchmarks are also used for funds with value-preserving strategies and Mr. K. additionally lists cash-flow based benchmarks that are used in connection with funds being managed against a certain liability structure. While the Information Ratio is very sensitive to the selected benchmark (cf. Chapter 4.3), it seems that portfolio management is very sophisticated in this field and should, therefore, not have any particular issues. In terms of evaluation intervals, portfolio managers are usually assessed on a monthly and yearly basis. While this study has worked exclusively with yearly Information Ratios based on the results of Chapter 4.4, monthly Information Ratios would in any case require daily return data. Information Ratios should be annualized according to the methods described in Goodwin (1998, pp. 37-39). All four portfolio managers are satisfied with the current performance evaluation system in the way that it is able to provide a true and fair view of the manager’s performance, which is also comprehensible by the client. However, according to Mr. K., it lacks a long-term and risk adjusted view in certain cases. This corresponds to the findings of

Copyright © 2010. Diplomica Verlag. All rights reserved.

Section 4.6 of the empirical study, where the importance of performance persistence or satisfactory performance over a longer time horizon is highlighted to separate the lucky from the skilled managers. Mr. R. highlights that in cases of severe market conditions, performance measurement against an index benchmark might not be in all cases consistent with the risk-bearing capabilities of the investors. This is a very important point, which applies to all relative performance measures, such as the Information Ratio. Because such an issue is usually not discussed in academic literature, it is important to ask 56

Fund Performance Measurement

practitioners about their experience. If the investor has certain absolute loss limits, for example a loss of up to 10% per year, then the Information Ratio would not be an adequate performance measure. One could imagine a scenario in which the benchmark loses 30% year-over-year but the actively managed fund is able to generate an excess performance of 10%. Without taking into account the tracking error, an active return of 10% would be a very good result in these market conditions. However, when looking at the absolute result, the fund lost 20% of its value in this scenario, which would be unacceptable for certain investors. Especially retail investors, but also non-profit organizations will have maximum absolute loss limits, which restrict the use of relative performance measures. In many cases, these funds employ option-based strategies, which lead to asymmetric return profiles. As explained in Sections 4.5 and 4.7, the Information Ratio is not able to correctly deal with non-normal return distributions. When questioned about the usefulness of the Information Ratio as a performance measure, two of the four portfolio managers mentioned the fund ranking problem in case of a negative numerator, that is negative excess return. This problem has also been extensively analyzed in Section 4.2 and it is important to see a similar awareness in practice. Using certain modified ratios as described and tested in the empirical study, this problem can be circumvented. It is also generally acknowledged by the four fund managers that the implementation of the Information Ratio as a sole performance measure can lead to a more passive approach (closet indexing) in portfolio management in order to boost the Information Ratio. This problem has been analyzed with an agency theoretic view in Section 2.4. While all questioned practitioners would not change their investment strategies simply to increase the Information Ratio, it is generally agreed that certain groups would intentionally act in this way, and that certain restrictions have to be put in place in order to prevent such actions. Mr. K., therefore, presents several options. Firstly, he suggests an integrated approach that uses a combination of the Sharpe Ratio Copyright © 2010. Diplomica Verlag. All rights reserved.

and the Information Ratio so that the strengths of both measures come to play. Recalling facts presented in Sections 2.1.3 and 2.2, the Sharpe Ratio uses total risk in the denominator, while the Information Ratio only considers the residual risk of the fund. Secondly, Mr. K. suggests the introduction of a minimum tracking error of 3% annually, so that all fund managers are forced to assume a certain level of active risk. The problem of closet indexing has been resolved in the performance evaluation framework proposed in this paper quite similarly by using the Active Share measure of Cremers & Petajisto 57

Fund Performance Measurement

(2007, pp. 6-7) and requiring a certain level of active weights, which force portfolio managers to take a certain percentage of active positions versus the benchmark. While the minimum tracking error is a more indirect approach, the Active Share explicitly requires over- or underweighting of securities and also encourages the diversification of active weights. Mr. K. also adds that he favors the Information Ratio over other ratios as it allows for good comparability of the manager’s active performance across different fund types and asset classes. While this is confirmed by the results of this study for funds of the same category, due care should be used when comparing Information Ratios without adjustments across different asset classes (cf. Chapter 4.1). This is especially important as Transfer Coefficients vary across asset classes and fund types due to investment restrictions, and, therefore, aggravate the comparability of Information Ratios. In the next step, the view of the head of performance evaluation, Ms. K., is analyzed. The following results are based on the fifth questionnaire, which can also be found in Appendix B. According to Ms. K., the performance evaluation is divided into three separate parts. Firstly, the performance measurement evaluates the fund on a daily basis using absolute and relative returns, as well as other measures, in particular the Information Ratio. These figures are calculated including and excluding management fees. Secondly, the performance attribution clarifies the sources of returns, such as asset allocation, security selection, currency gains or losses, and other contributors for funds of funds or downside protected portfolios. This is a very important aspect in order to verify that each fund is managed according to its specific objectives. Thirdly, peer group analyses compare the performance of the own funds with similar funds of competitors. Differences in the performance measurement methodology are mainly caused by different types of funds, by different asset classes and investment strategies, and by symmetric and asymmetric portfolios. A performance history based on the previous three years is Copyright © 2010. Diplomica Verlag. All rights reserved.

used together and equally weighted with the results of the current year. While this paper is focused mainly on the usefulness of the Information Ratio to evaluate the performance of portfolio managers, it now becomes clear that, from a practical perspective, there are many more factors influencing the overall performance, for example absolute return measures or results of the performance attribution versus the fund’s objectives. Ms. K. highlights that an evaluation of own funds against peers is important but not the single most important point. As already explained by the four portfolio managers, many 58

Fund Performance Measurement

customers (especially retail investors) care about absolute returns, but not so much about peer-group rankings. Therefore, absolute return measures will always play an important role. Internally, however, peer-group comparisons are important and also help to evaluate the competitors from the viewpoint of the customer. The Information Ratio is found to be a reliable measure and, in fact, is used in the dayto-day business. In line with the findings of this empirical study (cf. Chapter 4.5), Ms. K. suggests the use of this ratio only for asset classes that are showing return distributions close to a normal distribution. Other requirements from a practical perspective are adequate benchmarks, valuation or pricing of fund and benchmark at similar points in time, and fund returns net of all fees that are not caused by the manager. Especially the last requirement points to a drawback of this study. Only raw returns of the funds, including all fees were available to the author, so that fund managers with different fee structures are not treated equally. The Sortino Ratio and the underlying concept of downside risk is well known in fund administration, but its practical use is limited due to a lack of integration into computer systems. Its potential usefulness for asymmetric funds, which is also highlighted in Section 2.1.5 of this paper, has not yet been thoroughly evaluated in practice. This is also a sign that newly developed measures, such as the Omega Measure (cf. Chapter 2.1.7) by Keating & Shadwick (2002), need to prove their quality and usefulness before they gain popularity within the industry and are implemented in computer systems. This process takes some time but is also a form of quality assurance. The empirical study already showed that the data frequency plays a major role when it comes to the quality of performance measures (cf. Chapter 4.4). Ms. K. points out that weekly return data is used to calculate Information Ratios and also other performance measures. Daily data has been found to show inaccuracies and disturbances according to

Copyright © 2010. Diplomica Verlag. All rights reserved.

the tests of the performance analysis team. Additionally, excess returns and tracking errors are calculated on a rolling basis in order to smoothen out possible daily patterns especially of the tracking error. In general, the use of weekly data has proven successful in this study, and this was also confirmed by practitioners. Another important aspect in practical performance measurement is the data quality and availability, especially in the fixed-income asset class. The author of this study faced the

59

Fund Performance Measurement

same problem. This is why the data selection process had to be described extensively in Section 3 in order to be reproducible. Overall, the questionnaires provide valuable insights into the practical aspects of fund management and performance evaluation that complement the results of the empirical study. It is encouraging to receive confirmation of empirical results from experienced practitioners, and it is also valuable to clarify practical limits and requirements that are sometimes suppressed or ignored in academic analyses. The practical perspective also opens up new ideas for future research by extending certain academic questions.

6

Conclusion

The main motivation of this thesis was to evaluate whether the Information Ratio is a useful and reliable measure of the performance of portfolio managers. Based on the evidence gained from a theoretical as well as empirical perspective, it can be concluded that the Information Ratio, in fact, is reliable and useful, but with certain limitations. These limitations include issues with non-normally distributed fund returns, false rankings in connection with negative excess returns, the requirement of a sufficiently high data frequency, and a high sensitivity to the selected benchmark. It has been derived theoretically that useful and reliable performance measures are stable, precise, and correctly evaluate the service that is provided by the portfolio manager (Chen & Knez, 1996, pp. 511-513; Hübner, 2007, p. 65). According to the empirical results, the Information Ratio is more stable over time compared to other measures and able to precisely show the manager’s performance in terms of active management skills. It has been found, that “good” performance in terms of the Information Ratio cannot be determined on an absolute level but only relative to a peer group of funds with similar characteristics. The study, therefore, provides tables for the past 11 years that help to evaluate InCopyright © 2010. Diplomica Verlag. All rights reserved.

formation Ratios for certain fund categories. Additionally, persistence of Information Ratios over time helps to separate skilled from lucky managers. For a practical application of the framework developed in Sub-section 4.7, company and fund specific qualitative measures should also be incorporated. Based on the evidence presented in Section 5, it is clear that many of the assumptions of the empirical study are valid, and that the results, in fact, can be used in practical applications.

60

Fund Performance Measurement

While the results, especially of the empirical analysis, are able to answer many of the research questions raised in the beginning of this study, they also open up new issues. This is due to the fact that the analyses were subject to certain limitations and some results were not as one would have expected them to be at first glance. Although the dataset contains nearly 10,000 individual funds and covers a time frame from January 1, 1998 through December 31, 2008, it is subject to certain limitations in its quality. Firstly, the returns are not corrected for management and administration fees, so that the performance is biased in a way. As mentioned by Ms. K. (cf. Appendix B, fifth questionnaire), the active performance of the manager should be (and in practice is) measured using returns that are net of fees. In fact, a significant part of the total fees cannot be influenced by the portfolio managers, for example fund audit or custody fees have to be paid in any case (Wilcox, 2005). Unfortunately, information about fund specific management and administration fees was not available to the author of this thesis. It is, therefore, recommended to conduct additional studies in order to test if the threshold values for “very good”, “good”, “below average”, and “poor” funds change significantly when using net returns. Secondly, the number of funds in the asset classes fixed income and money market is rather low, compared to the equity class. According to Table 1, the sample in 2008 contains 8,131 funds that invest in equity securities, 644 funds that invest in fixed income securities, and 857 funds that invest in money market securities. Additionally, the sample is dominated by funds investing in the US. This is mainly caused by the fact that the US is a larger economic area than Germany, UK or parts of the European Union. The domination of equity funds and funds investing in the US in this sample is, however, mainly caused by the data providers that were used for this study: Thomson Financial DataStream and Reuters 3000 Xtra. Other data providers, such as Morningstar that were not accessible to the author could have been used to retrieve more balanced datasets or datasets with a different market focus. Thirdly, many Copyright © 2010. Diplomica Verlag. All rights reserved.

funds are subject to style drifts, that is the fund management changes its investment universe from time to time in the hope of recouping past losses or to exploit new opportunities (Chan et al., 2002, p. 1410). This action generally causes the fund to be categorized differently and past fund returns cannot be easily compared with the returns of funds of the new category. This study uses the LGC sector classification to filter and select funds, but there was only access to the latest LGC classification of each fund. Therefore, it was not possible to track style drifts of the funds. Although the fund cate61

Fund Performance Measurement

gories, such as “Equity Europe” or “Corporate Bonds USD”, were selected because they generally show very little style drift due to the large investment universe, it would be interesting to test for biases caused by style drift in continuative papers. Fourthly, as explained in Section 3.1 and analyzed in Section 4.5, the sample is subject to survivorship bias. This is the result of poor funds being closed completely, or being merged into other funds over time so that their return track records disappear from the databases. According to literature, the survivorship bias can be up to 0.8% per year and, therefore, influence the performance measures that are calculated based on these returns (Brown et al., 1995). As the author did not have access to an unbiased dataset, it is suggested to explore the effects of survivorship bias on performance measures in future research. In addition to the dataset, the analyses created ideas for additional research. Firstly, the author used a generic benchmark for each fund category, and also explained in Section 3.2, why this was determined a suitable method. It would, however, be interesting to compare the results based on a generic benchmark with results that are calculated with fund-specific benchmarks determined by the portfolio managers. Unfortunately, it was not possible to retrieve information about the specific benchmark for each fund within the scope of this study. Secondly, it is suggested to analyze Information Ratios of funds with more specific style definitions, such as “US value stocks” or “European bank stocks”. It is expected that there are major differences in Information Ratios between these styles. However, the number of funds investing in such specialized sectors is rather small, which will affect the significance of the results. Thirdly, the effect of the Transfer Coefficient on the manager’s active performance should be analyzed in more detail. As already introduced in Section 4.1, managers of mutual funds face certain investment restrictions that prevent the allocation of funds to the best possible portfolio. These restrictions will negatively affect the Information Ratio, although they are not influenceable by the manager. According to Wander (2003), mutual funds can face TCs Copyright © 2010. Diplomica Verlag. All rights reserved.

of 0.5 or even lower, and, therefore, the manager would have to double his performance in order to be as good as an unconstrained portfolio manager. Future research could develop and empirically analyze ways to modify performance measures so that the impact of investment restrictions is neutralized across different funds. Fourthly, the results of this study could be extended by analyzing performance measures that incorporate higher moments, such as the Omega Measure (cf. Chapter 2.1.7). It would be interesting

62

Fund Performance Measurement

to explore their strength and weaknesses using standard mutual funds and funds with protection levels or other asymmetric payoff profiles. Mutual fund performance measurement has been at the center of academic interest since the formation of the first investment companies and will always continue to be relevant for investors as well as researchers (Jensen, 1968, p. 389). As the perfect way of performance measurement is yet unknown, it is important to evaluate the advantages and disadvantages of the performance measures that are available today (Baks et al., 2001, p. 73). This thesis is able to shed light on many questions and issues related to the use of the Information Ratio. Since Treynor & Black developed this measure in 1973, many other more powerful and more complex performance measures have been presented. Still, the Information Ratio is one of the best known and most widely used ratios to evaluate the performance of active fund managers today (Grinold, 1989, p. 31). It is easy to understand, comprehensible, and can be calculated without using complex mathematics. Most likely these properties are more important in the day-to-day use of performance measures than a slightly better power of another ratio that comes at cost of difficult calculation steps and other potential limitations. The simplicity and understandability of the Omega Measure developed by Keating & Shadwick (2002) could be one of the most important factors besides its power that help to increase the popularity of this measure among investment managers in the future. When evaluating performance measures, it should always be kept in mind that in practical applications usability and understandability is often more important than a slightly higher precision. This is the reason why

Copyright © 2010. Diplomica Verlag. All rights reserved.

the Information Ratio is still very popular in the industry and in academia.

63

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

List of References Ackermann, C., McEnally, R., & Ravenscraft, D. (1999). The Performance of Hedge Funds: Risk, Return and Incentives [Electronic version]. The Journal of Finance, 54(3), 833-874. Akeda, Y. (2003). Another Interpretation of Negative Sharpe Ratio [Electronic version]. Journal of Performance Measurement, 7(3), 19-23. Ané, T., & Labidi, C. (2004). Return Interval, Dependence Structure, and Multivariate Normality [Electronic version]. Journal of Economics and Finance, 28(3), 285299. Baks, K. P., Metrick, A., & Wachter, J. (2001). Should Investors Avoid All Actively Managed Mutual Funds? A Study in Bayesian Performance Evaluation [Electronic version]. The Journal of Finance, 56(1), 45-85. Below, S. D., & Stansell, S. R. (2003). Do the individual moments of REIT return distributions affect institutional ownership patterns? [Electronic version]. Journal of Asset Management, 4(2), 77-95. Benders, R. (2009, February 26). Kritiker greifen den Dow an. Handelsblatt, p. 28. Benson, K., Gray, P., Kalotay, E., & Qiu, J. (2008). Portfolio Construction and Performance Measurement when Returns are Non-Normal [Electronic version]. Australian Journal of Management, 32(3), 445-461. Bodie, Z., Kane, A., & Marcus, A. J. (2005). Investments. (6th ed.). New York, NY: McGraw-Hill. Bollen, N. P. B., & Busse, J. A. (2005). Short-Term Persistence in Mutual Fund Performance [Electronic version]. The Review of Financial Studies, 18(2), 569-597. British Bankers' Association. (2002). The BBA LIBOR fixing & definition. British Bankers' Association & BBA Enterprises Ltd. Retrieved February 13, 2009, from http://www.bba.org.uk/bba/jsp/polopoly.jsp?d=225&a=1413 Brown, S. J., Goetzmann, W., Ibbotson, R. G., & Ross, S. A. (1992). Survivorship Bias in Performance Studies [Electronic version]. The Review of Financial Studies, 5(4), 553-580. Brown, S. J., & Goetzmann, W. N. (1995). Performance Persistence [Electronic version]. The Journal of Finance, 50(2), 679-698.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Brown, S. J., Goetzmann, W. N., & Ross, S. A. (1995). Survival [Electronic version]. The Journal of Finance, 50(3), 853-873. Carhart, M. M. (1997). On Persistence in Mutual Fund Performance [Electronic version]. The Journal of Finance, 52(1), 57-82. Chan, L. K. C., Chen, H.-L., & Lakonishok, J. (2002). On Mutual Fund Investment Styles [Electronic version]. The Review of Financial Studies, 15(5), 1407-1437. Chaudhry, A., & Johnson, H. L. (2008). The Efficacy of the Sortino Ratio and Other Benchmarked Performance Measures Under Skewed Return Distributions [Electronic version]. Australian Journal of Management, 32(3), 485-502. 65

Fund Performance Measurement

Chen, Z., & Knez, P. J. (1996). Portfolio Performance Measurement: Theory and Applications [Electronic version]. The Review of Financial Studies, 9(2), 511-555. Cohen, J. (1960). A coefficient of agreement for nominal scales [Electronic version]. Educational and Psychological Measurement, 20(1), 37-46. Cranshaw, T. E. (1977). The Evaluation of Investment Performance [Electronic version]. The Journal of Business, 50(4), 462-485. Cremers, M., & Petajisto, A. (2007, January). How Active is Your Fund Manager? A New Measure That Predicts Performance. Paper presented at the Annual Meeting of the American Finance Association, Chicago, IL. Cummings, N. (2008). How to tackle low Libor? [Electronic version]. International Financial Law Review, 27(11), 61-63. D'Agostino, R. B. (1970). Linear Estimation of the Normal Distribution Standard Deviation [Electronic version]. The American Statistician, 24(3), 14-15. Deutsche Börse AG. (2009). Leitfaden zu den Aktienindizes der Deutschen Börse. Frankfurt am Main. Dow Jones Indexes. (2009). The Dow Jones Industrial Average. Dow Jones Indexes. Retrieved February 20, 2009, from http://www.djaverages.com/?view=industrial&page=overview Elton, E. J., Gruber, M. J., & Blake, C. R. (1996). Survivorship Bias and Mutual Fund Performance [Electronic version]. The Review of Financial Studies, 9(4), 10971120. Estrada, J. (2006). Downside Risk in Practice [Electronic version]. Journal of Applied Corporate Finance, 18(1), 117-125. Eveillard, J.-M. (2000). Benchmark Tyranny [Electronic version]. Financial Planning, 30(11), 224. Fama, E. F., & French, K. R. (1993). Common Risk Factors in the Returns on Stocks and Bonds [Electronic version]. Journal of Financial Economics, 33(1), 3-56. FTSE International. (2009a). FTSE 100 Index Fact Sheet. London. FTSE International. (2009b). FTSE All Share Index Fact Sheet. London. Golec, J. H. (1992). Empirical Tests of a Principal-Agent Model of the InvestorInvestment Advisor Relationship [Electronic version]. The Journal of Financial and Quantitative Analysis, 27(1), 81-95.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Goodwin, T. H. (1998). The Information Ratio [Electronic version]. Financial Analysts Journal, 54(4), 34-43. Grinblatt, M., & Titman, S. (1989a). Adverse Risk Incentives and the Design of Performance-Based Contracts [Electronic version]. Management Sciences, 35(7), 807-822. Grinblatt, M., & Titman, S. (1989b). Mutual Fund Performance: An Analysis of Quarterly Portfolio Holdings [Electronic version]. The Journal of Business, 62(3), 393-416. Grinblatt, M., & Titman, S. (1992). The Persistence of Mutual Fund Performance [Electronic version]. The Journal of Finance, 47(5), 1977-1984. 66

Fund Performance Measurement

Grinblatt, M., & Titman, S. (1993). Performance Measurement without Benchmarks: An Examination of Mutual Fund Returns [Electronic version]. The Journal of Business, 66(1), 47-68. Grinold, R. C. (1989). The fundamental law of active management [Electronic version]. Journal of Portfolio Management, 15(3), 30-37. Grinold, R. C., & Kahn, R. N. (2000). Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk. (2nd ed.). New York, NY: McGraw-Hill. Handa, P., Kothari, S. P., & Wasley, C. (1989). The Relation Between the Return Interval and Betas: Implications for the Size Effect [Electronic version]. Journal of Financial Economics, 23(1), 79-100. Hollander, M., & Wolfe, D. A. (1973). Nonparametric Statistical Methods. Hoboken, NJ: John Wiley & Sons, Inc. Holmstrom, B. (1979). Moral hazard and observability [Electronic version]. Bell Journal of Economics, 10(1), 74-91. Horowitz, I. (1966). The "Reward-to-Variability" Ratio and Mutual Fund Performance [Electronic version]. The Journal of Business, 39(4), 485-488. Horst, J. t., & Verbeek, M. (2000). Estimating Short-Run Persistence in Mutual Fund Performance [Electronic version]. The Review of Economics and Statistics, 82(4), 646-655. Hübner, G. (2005). The Generalized Treynor Ratio [Electronic version]. Review of Finance, 9(3), 415-435. Hübner, G. (2007). How Do Performance Measures Perform? [Electronic version]. Journal of Portfolio Management, 33(4), 64-74. Investment Company Institute. (2008). Investment Company Fact Book 2008 - A Review of Trends and Activity in the Investment Company Industry. (48th ed.). Washington, DC. Israelsen, C. L. (2003). Sharpening the Sharpe Ratio [Electronic version]. Financial Planning, 33(1), 49-51. Israelsen, C. L. (2005). A refinement to the Sharpe ratio and information ratio [Electronic version]. Journal of Asset Management, 5(6), 423-427.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Israelsen, C. L., & Cogswell, G. F. (2007). The Error of Tracking Error [Electronic version]. Journal of Asset Management, 7(6), 419-424. Jacobs, B. I., & Levy, K. N. (1996). Residual Risk: How Much is Too Much? [Electronic version]. Journal of Portfolio Management, 21(3), 10-16. Jensen, M. C. (1968). The Performance of Mutual Funds in the Period 1945-1964 [Electronic version]. The Journal of Finance, 23(2), 389-416. Jobson, J. D., & Korkie, B. M. (1981). Performance Hypothesis Testing with the Sharpe and Treynor Measures [Electronic version]. The Journal of Finance, 36(4), 889908. Kahn, R. N., & Rudd, A. (1995). Does Historical Performance Predict Future Performance? [Electronic version]. Financial Analysts Journal, 51(6), 43-52. 67

Fund Performance Measurement

Keating, C., & Shadwick, W. F. (2002). Omega: A Universal Performance Measure [Electronic version]. Journal of Performance Measurement, 6(3), 59-84. Kjetsaa, R. (2004). Actively Managed Equity Mutual Fund Performance Relative to Benchmarks [Electronic version]. American Business Review, 22(1), 102-112. Kothari, S. P., & Warner, J. B. (2001). Evaluating Mutual Fund Performance [Electronic version]. The Journal of Finance, 56(5), 1985-2010. Kraus, A., & Litzenberger, R. H. (1976). Skewness Preference and the Valuation of Risk Assets [Electronic version]. The Journal of Finance, 31(4), 1085-1100. Lehmann, B. N., & Modest, D. M. (1987). Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons [Electronic version]. The Journal of Finance, 42(2), 233-265. Levy, R. A. (1968). Measurement of Investment Performance [Electronic version]. The Journal of Financial and Quantitative Analysis, 3(1), 35-57. Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown [Electronic version]. Journal of the American Statistical Association, 62(318), 399-402. Lin, L. I.-K. (1989). A Concordance Correlation Coefficient to Evaluate Reproducibility [Electronic version]. Biometrics, 45(1), 255-268. Lin, L. I.-K. (2000). A Note on the Concordance Correlation Coefficient [Electronic version]. Biometrics, 56(1), 324-325. Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets [Electronic version]. Review of Economics and Statistics, 47(1), 13-37. Lipper/Thomson Reuters. (2005). Lipper Global Classification 2005 - Definitions Document. Lipper/Thomson Reuters. Retrieved February 13, 2009, from http://www.lipperweb.com/common/dm-content.asp?docTag= PDF1125498332156 Lo, A. W. (2002). The Statistics of Sharpe Ratios [Electronic version]. Financial Analysts Journal, 58(4), 36-52. Mahdavi, M. (2004). Risk-Adjusted Return When Returns Are Not Normally Distributed: Adjusted Sharpe Ratio [Electronic version]. Journal of Alternative Investments, 6(4), 47-57.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Malkiel, B. G. (1995). Returns from Investing in Equity Mutual Funds 1971 to 1991 [Electronic version]. The Journal of Finance, 50(2), 549-572. Markowitz, H. (1952). Portfolio Selection [Electronic version]. The Journal of Finance, 7(1), 77-91. McGill, R., Tukey, J. W., & Larsen, W. A. (1978). Variations of Box Plots [Electronic version]. The American Statistician, 32(1), 12-16. Modigliani, F., & Modigliani, L. (1997). Risk-Adjusted Performance [Electronic version]. Journal of Portfolio Management, 23(2), 45-54. Moy, R. L. (2002). Portfolio Performance: Illustrations From Morningstar [Electronic version]. Journal of Education for Business, 77(4), 226-229. 68

Fund Performance Measurement

MSCI Barra. (2009). MSCI Barra Index Definitions. MSCI Barra. Retrieved February 13, 2009, from http://www.mscibarra.com/products/indices/equity/definitions.jsp Muralidhar, A. S. (2000). Risk-Adjusted Performance: The Correlation Correction [Electronic version]. Financial Analysts Journal, 56(5), 63-71. Padgette, R. L. (1995). Performance Reporting: The Basics and Beyond, Part II [Electronic version]. Journal of Financial Planning, 8(4), 172-180. Pedersen, C. S., & Satchell, S. E. (2002). On the Foundation of Performance Measures Under Asymmetric Returns [Electronic version]. Quantitative Finance, 2(3), 217-223. Ross, S. A. (1973). The Economic Theory of Agency: The Principal's Problem [Electronic version]. American Economic Review, 63(2), 134-139. Russell Investment Group. (2009). Russel 1000 Index. Tacoma, WA. Scholz, H. (2006). Refinements to the Sharpe ratio: Comparing alternatives for bear markets [Electronic version]. Journal of Asset Management, 7(5), 347-357. Scholz, H., & Wilkens, M. (2006). The Sharpe Ratio's Market Climate Bias - Theoretical and Empirical Evidence from US Equity Mutual Funds. Unpublished Working Paper. Catholic University of Ingolstadt. Sharpe, W. F. (1964). Capital Asset Prices: A Theory for Market Equilibrium Under Conditions of Risk [Electronic version]. The Journal of Finance, 19(3), 425442. Sharpe, W. F. (1966). Mutual Fund Performance [Electronic version]. The Journal of Business, 39(1), 119-138. Sharpe, W. F. (1975). Adjusting for Risk in Portfolio Performance Measurement [Electronic version]. Journal of Portfolio Management, 1(2), 29-34. Sharpe, W. F. (1994). The Sharpe Ratio [Electronic version]. Journal of Portfolio Management, 21(1), 49-58. Sharpe, W. F. (1998). Morningstar's Risk-adjusted Ratings [Electronic version]. Financial Analysts Journal, 54(4), 21-33. Sortino, F. A., & Price, L. N. (1994). Performance Measurement in a Downside Risk Framework [Electronic version]. The Journal of Investing, 3(3), 50-58. Standard & Poor's. (2009a). S&P 500 Index Methodology. New York, NY.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Standard & Poor's. (2009b). S&P 600 Small Cap Index Methodology. New York, NY. Staub, R. (2007). Are you about to handcuff your information ratio? [Electronic version]. Journal of Asset Management, 7(5), 358-370. Stoughton, N. M. (1993). Moral Hazard and the Portfolio Management Problem [Electronic version]. The Journal of Finance, 48(5), 2009-2028. Stutzer, M. (2000). A Portfolio Performance Index [Electronic version]. Financial Analysts Journal, 56(3), 52-61. Treynor, J. L. (1961). Toward a Theory of Market Value of Risky Assets. Working Paper. Subsequently published in R. A. Korajczyk (1999). Asset Pricing and Port69

Fund Performance Measurement

folio Performance: Models, Strategy and Performance Metrics. London: Risk Books. Treynor, J. L. (1965). How to Rate Management of Investment Funds [Electronic version]. Harvard Business Review, 43(1), 63-75. Treynor, J. L., & Black, F. (1973). How to Use Security Analysis to Improve Portfolio Selection [Electronic version]. The Journal of Business, 46(1), 66-86. Wander, B. H. (2003). What it Takes to Beat a Benchmark [Electronic version]. The Journal of Investing, 12(3), 37-42. Wermers, R. (2000). Mutual Fund Performance: An Empirical Decomposition into Stock-Picking Talent, Style, Transaction Costs, and Expenses [Electronic version]. The Journal of Finance, 55(4), 1655-1695. Wilcox, R. T. (2005). Developing Better Fee Structures for Mutual Funds [Electronic versions]. Journal of Investment Management, 3(2), 12-23.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Wolde, R. C. (1998, September 2). Balanced funds grow in popularity, aided by volatility in stock market. Wall Street Journal - Eastern Edition, p. B7C.

70

Fund Performance Measurement

Appendix A Figure 15: Distribution of Information Ratios Based on Different Data Frequencies

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations

71

Money Market EUR

Corporate Bonds USD

Corporate Bonds GBP

Corporate Bonds EUR

Equity Small Cap US

Equity Small Cap UK

Equity Small Cap Europe

Equity US

Equity UK

Equity Germany

Equity Europe

> 0.33

N/A

> -0.37

> 0.56

N/A

> 0.65

> -0.92

> 0.04

> -0.39

> -0.26

> 0.02

> 0.23

1998

> 1.50

> 1.10

N/A

> 0.26

> -0.04

N/A

> 1.50

> 2.50

> 2.40

> 0.36

> 0.79

> -0.16

> 1.30

1999

> 1.40

> 1.20

N/A

> 0.46

> -0.64

N/A

> -0.26

> 0.67

> 0.60

> 0.66

> 0.62

> 0.44

> 0.38

2000

> 5.90

> 4.60

N/A

> -0.64

> -0.50

N/A

> -0.21

> 0.19

> -0.21

> 0.51

> 0.24

> 0.21

> 0.15

2001

> 3.00

> 5.90

> 4.60

> -0.28

> -0.19

> 0.08

> 0.06

> 0.25

> 0.50

> 0.71

> 0.15

> 0.35

> 0.28

2002

> 5.20

> 5.60

> 7.70

> -0.01

> -0.17

> -0.30

> 0.44

> 1.30

> 1.40

> 0.36

> 0.65

> 0.12

> -0.12

2003

> 2.70

> 3.70

> 7.40

> -0.26

> 0.07

> -0.95

> -0.74

> 1.40

> 1.70

> 0.18

> 0.44

> -0.14

> 0.46

2004

> 0.98

> 10.00

> 7.80

> -0.08

> -0.15

> -0.32

> -0.05

> 0.47

> 1.60

> 0.55

> 0.31

> -0.02

> 0.91

2005

> 2.10

> 7.90

> 4.20

> 0.00

> -0.08

> 0.26

> -0.49

> 1.50

> 1.60

> -0.38

> 0.58

> 0.08

> 0.81

2006

> 1.30

> 3.80

> 0.51

> 0.49

> 0.30

> 0.63

> 0.49

> -0.68

> -0.28

> 0.44

> -0.23

> -0.22

> -0.09

2007

> 1.20

> 3.20

> 0.04

> 0.71

> 1.20

> -1.10

> -0.52

> -0.18

> -0.49

> 0.08

> 0.18

> 0.11

> 0.08

2008

Fund Classification

Money Market GBP

> 1.80

72

Money Market USD

Source: Own calculations

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

Table 12: Information Ratio – Threshold Values for 1st Quartile Funds (very good)

Money Market GBP

Money Market EUR

Corporate Bonds USD

Corporate Bonds GBP

Corporate Bonds EUR

Equity Small Cap US

Equity Small Cap UK

Equity Small Cap Europe

Equity US

Equity UK

Equity Germany

Equity Europe

1.80 to 0.62

0.33 to -0.08

N/A

-0.37 to -0.67

0.56 to .0.10

N/A

0.65 to -0.09

-0.92 to -1.20

0.04 to -0.39

-0.39 to -1.20

-0.26 to -0.52

0.02 to -0.15

0.23 to 0.01

1998

1.50 to 0.10

1.10 to -0.01

N/A

0.26 to -0.31

-0.04 to -0.27

N/A

1.50 to 0.39

2.50 to 1.90

2.40 to 2.00

0.36 to -0.71

0.79 to 0.21

-0.16 to -0.27

1.30 to 0.80

1999

1.40 to 0.55

1.20 to -1.20

N/A

0.46 to -0.09

-0.64 to -0.95

N/A

-0.26 to -0.82

0.67 to 0.45

0.60 to 0.29

0.66 to -0.07

0.62 to 0.32

0.44 to 0.25

0.38 to -0.06

2000

5.90 to 2.20

4.60 to 0.71

N/A

-0.64 to -1.10

-0.50 to -0.91

N/A

-0.21 to -1.10

0.19 to -0.16

-0.21 to -0.89

0.51 to -0.18

0.24 to -0.03

0.21 to 0.01

0.15 to -0.14

2001

3.00 to 1.20

5.90 to 0.72

4.60 to 2.00

-0.28 to -0.92

-0.19 to -0.50

0.08 to -0.25

0.06 to -0.67

0.25 to -0.17

0.50 to 0.04

0.71 to -0.07

0.15 to -0.05

0.35 to 0.14

0.28 to -0.06

2002

5.20 to 1.50

5.60 to 1.20

7.70 to 2.70

0.00 to -1.00

-0.17 to -0.64

-0.30 to -0.71

0.44 to -0.19

1.30 to 1.00

1.40 to 1.10

0.36 to -0.22

0.65 to 0.26

0.12 to -0.03

-0.12 to -0.39

2003

2.70 to 0.03

3.70 to 0.82

7.40 to 3.20

-0.26 to -0.80

0.07 to -0.41

-0.95 to -1.40

-0.74 to -1.10

1.40 to 1.00

1.70 to 1.30

0.18 to -0.36

0.44 to 0.08

-0.14 to -0.26

0.46 to 0.02

2004

0.98 to -0.73

10.00 to 1.10

7.80 to 2.00

-0.08 to -0.41

-0.15 to -0.77

-0.32 to -0.66

-0.05 to -0.64

0.47 to -0.01

1.60 to 1.10

0.55 to -0.09

0.31 to -0.01

-0.02 to -0.21

0.91 to 0.53

2005

2.10 to 0.14

7.90 to 0.57

4.20 to 1.00

0.00 to -0.49

-0.08 to -0.45

0.26 to -0.01

-0.49 to -0.92

1.50 to 0.95

1.60 to 1.30

-0.38 to -0.90

0.58 to 0.25

0.08 to -0.08

0.81 to 0.45

2006

1.30 to -0.10

3.80 to 0.02

0.51 to -1.00

0.49 to 0.03

0.30 to -0.34

0.63 to -0.09

0.49 to -0.29

-0.68 to -0.98

-0.28 to -0.66

0.44 to -0.33

-0.23 to -0.52

-0.22 to -0.39

-0.09 to -0.45

2007

1.20 to -1.30

3.20 to -0.37

0.04 to -1.70

0.71 to -0.55

1.20 to 0.05

-1.1 to -2.2

-0.52 to -1.20

-0.18 to -0.44

-0.49 to -0.87

0.08 to -0.35

0.18 to -0.06

0.11 to -0.16

0.08 to -0.29

2008

Fund Classification

Money Market USD

Source: Own calculations

73

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

Table 13: Information Ratio – Threshold Values for 2nd Quartile Funds (good)

Fund Performance Measurement

Table 14: Test Statistics for Information Ratios of Equity US Funds 1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

0.052*

0.079*

0.049*

0.023*

0.042*

0.042*

0.049*

0.034*

0.029*

0.063*

0.057*

Source: Own calculations * = significantly different from normal distribution (Lilliefors test, level of significance = 5%)

Table 15: Test Statistics for Information Ratios of Selected US Funds Year

Equity

Small Cap Equity

Fixed-Income

Money Market

1998

0.052*

0.039*

0.087*

0.465*

2008

0.057*

0.046*

0.090*

0.212*

Source: Own calculations * = significantly different from normal distribution (Lilliefors test, level of significance = 5%)

Table 16: Distribution Properties of Performance Measures for Equity US Funds Measure Sharpe Ratio

Information Ratio

Sortino Ratio

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations

74

Year

Mean

Std. Dev.

Skewness

Exc. Kurt.

1998

0.4588

0.6220

2.3497

35.1767

2008

-1.6334

1.4222

-47.5381

257.5200

1998

-1.0479

1.0816

0.4314

0.2858

2008

-0.3298

0.9391

0.2972

0.2363

1998

-1.2844

1.6140

2.1573

21.1941

2008

-0.3440

1.5702

1.1044

2.8631

Money Market GBP

Money Market EUR

Corporate Bonds USD

Corporate Bonds GBP

Corporate Bonds EUR

Equity Small Cap US

Equity Small Cap UK

Equity Small Cap Europe

Equity US

Equity UK

Equity Germany

Equity Europe

> 11.00

> 14.00

N/A

> 0.99

> 2.40

N/A

> 0.07

> -0.31

> 0.64

> 0.82

> 0.46

> 0.53

> 0.75

1998

> 12.00

> 1.90

N/A

> -0.82

> -0.65

N/A

> 1.40

> 4.20

> 3.30

> 1.00

> 1.50

> 1.30

> 1.90

1999

> 14.00

> 4.90

N/A

> 1.60

> 0.73

N/A

> 0.26

> 0.19

> 0.23

> -0.14

> -0.32

> -0.26

> -0.06

2000

> 3.50

> 2.90

N/A

> 0.99

> 0.26

N/A

> 0.10

> -0.86

> -1.20

> -0.55

> -0.88

> -0.71

> -0.89

2001

> -4.00

> -0.11

> 4.80

> 1.40

> 0.49

> 1.80

> -0.91

> -2.00

> -1.60

> -1.10

> -1.20

> -1.40

> -1.30

2002

> -8.50

> -1.20

> -0.33

> 1.30

> 0.71

> 1.40

> 1.90

> 2.40

> 1.80

> 1.50

> 1.10

> 0.92

> 0.54

2003

> -11.0

> 0.60

> -1.50

> 0.35

> 0.62

> 1.90

> 0.90

> 2.50

> 1.80

> 0.87

> 1.10

> 0.38

> 0.99

2004

> -0.32

> 1.70

> -1.80

> -0.25

> 0.95

> 0.42

> 0.39

> 2.10

> 2.90

> 0.46

> 1.80

> 2.00

> 2.30

2005

> 14.00

> 3.00

> 1.50

> 0.51

> -0.97

> -0.87

> 0.51

> 2.00

> 1.70

> 0.97

> 1.10

> 1.19

> 1.30

2006

> 14.00

> 11.00

> 7.00

> 0.51

> -0.88

> -1.30

> 0.14

> -0.47

> -0.11

> 0.38

> 0.09

> 1.10

> 0.02

2007

> -1.60

> 4.10

> 4.80

> -0.64

> -0.96

> -0.92

> -1.30

> -2.00

> -2.50

> -1.40

> -1.60

> -1.8

> -2.20

2008

Fund Classification

Money Market USD

Source: Own calculations

75

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

Table 17: Sharpe Ratio – Threshold Values for 1st Quartile Funds (very good)

Equity UK

Equity Germany

Equity Europe

0.82 to 0.48

0.46 to 0.33

0.53 to 0.44

0.75 to 0.64

1998

1.00 to 0.56

1.50 to 1.10

1.30 to 1.20

1.90 to 1.70

1999

-0.14 to -0.52

-0.32 to -0.59

-0.26 to -0.38

-0.06 to -0.37

2000

-0.55 to -0.78

-0.88 to -1.00

-0.71 to -0.80

-0.89 to -1.00

2001

-1.10 to -1.30

-1.20 to -1.40

-1.40 to -1.50

-1.30 to -1.40

2002

1.50 to 1.40

1.10 to 0.84

0.92 to 0.83

0.54 to 0.39

2003

1.80 to 1.50

0.87 to 0.66

1.10 to 0.87

0.38 to 0.31

0.99 to 0.71

2004

2.90 to 2.60

0.46 to 0.20

1.80 to 1.60

2.00 to 1.80

2.30 to 2.20

2005

1.70 to 1.50

0.97 to 0.60

1.10 to 0.92

1.19 to 1.10

1.30 to 1.20

2006

-0.11 to -0.32

0.38 to 0.02

0.09 to -0.09

1.10 to 0.92

0.02 to -0.17

2007

-2.50 to -2.70

-1.40 to -1.60

-1.60 to -1.70

-1.80 to -1.90

-2.20 to -2.30

2008

Fund Classification

Equity US

1.80 to 1.50

-1.30 to -1.40

-1.60 to -1.90

0.14 to -0.38

-0.92 to -1.60

-1.20 to -1.50

0.51 to 0.17

-1.30 to -1.70

-0.96 to -1.80

0.23 to -.0.1

0.39 to 0.06

-0.87 to -1.10

-0.88 to -1.30

-0.64 to -1.40

3.30 to 2.80

0.90 to 0.61

0.42 to 0.21

-0.97 to -1.20

0.51 to 0.19

4.80 to 0.01

0.64 to 0.44

1.90 to 1.70

1.90 to 1.70

0.95 to 0.67

0.51 to 0.26

7.00 to 1.70

4.10 to 0.41

-2.00 to -2.40 -0.91 to -1.20

1.40 to 1.00

0.62 to 0.25

-0.25 to -0.47

1.50 to -0.18

11.00 to 1.00

-0.47 to -0.73 0.10 to -0.34

1.80 to 1.50

0.71 to 0.35

0.35 to 0.14

-1.80 to -5.00

3.00 to -0.34

2.00 to 1.60 0.26 to -0.20

N/A

0.49 to 0.22

1.30 to 0.67

-1.50 to -4.20

1.70 to -0.51

-1.60 to -3.10

2.10 to 1.70 1.40 to 0.68

N/A

0.26 to 0.02

1.40 to 1.10

-0.33 to -1.30

0.60 to -1.30

14.00 to 1.50

2.50 to 2.10

0.07 to -0.22

N/A

0.73 to 0.39

0.99 to 0.79

4.80 to 2.10

-1.20 to -3.40

14.00 to 5.10

2.40 to 2.10

Equity Small Cap UK

N/A

-0.65 to -0.97

1.60 to 1.20

N/A

-0.11 to -2.60

-0.32 to -2.30

-2.00 to -2.30

Equity Small Cap US

2.40 to 2.00

-0.82 to -1.00

N/A

2.90 to 0.22

-11.0 to -23.0

-0.86 to -1.10

Corporate Bonds EUR

0.99 to 0.64

N/A

4.90 to 1.10

-8.50 to -

0.19 to -0.03

Corporate Bonds GBP

N/A

1.90 to 0.53

-4.00 to -8.30

4.20 to 3.60

Corporate Bonds USD

14.00 to 4.10

3.50 to 1.80

-0.31 to -0.56

Money Market EUR

14.00 to 7.90

Equity Small Cap Europe

Money Market GBP

12.00 to 4.50

20 00

11.00 to 4.80

76

Money Market USD

Source: Own calculations

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

Table 18: Sharpe Ratio – Threshold Values for 2nd Quartile Funds (good)

Money Market GBP

Money Market EUR

Corporate Bonds USD

Corporate Bonds GBP

Corporate Bonds EUR

Equity Small Cap US

Equity Small Cap UK

Equity Small Cap Europe

Equity US

Equity UK

Equity Germany

Equity Europe

> 3.20

> 3.00

N/A

> -0.61

> 1.10

N/A

> 0.97

> -1.30

> 0.06

> -0.56

> -0.43

> 0.04

> 0.41

1998

> 3.60

> 5.00

N/A

> 0.40

> -0.08

N/A

> 2.60

> 6.20

> 6.30

> 0.54

> 1.50

> -0.27

> 2.60

1999

> 4.00

> 3.10

N/A

> 0.86

> -1.10

N/A

> -0.37

> 1.30

> 0.96

> 1.10

> 1.10

> 0.74

> 0.68

2000

> 21.00

> 15.00

N/A

> -0.73

> -0.86

N/A

> -0.30

> 0.31

> -0.35

> 0.87

> 0.45

> 0.32

> 0.24

2001

> 10.00

> 21.00

> 12.00

> -0.46

> -0.33

> 0.14

> 0.09

> 0.39

> 0.86

> 1.30

> 0.23

> 0.55

> 0.46

2002

> 24.00

> 23.00

> 33.00

> -0.01

> -0.29

> -0.53

> 0.84

> 2.60

> 2.90

> 0.65

> 1.10

> 0.20

> -0.19

2003

> 7.10

> 14.00

> 32.00

> -0.36

> 0.11

> -1.40

> -1.00

> 2.70

> 3.30

> 0.29

> 0.78

> -0.21

> 0.78

2004

> 2.10

> 77.00

> 32.00

> -0.12

> -0.28

> -0.59

> -0.08

> 0.70

> 2.80

> 0.95

> 0.50

> -0.03

> 1.60

2005

> 4.60

> 42.00

> 11.00

> 0.00

> -0.13

> 0.44

> -0.66

> 2.50

> 2.50

> -0.54

> 0.95

> 0.11

> 1.30

2006

> 3.30

> 8.30

> 0.87

> 0.84

> 0.52

> 1.10

> 0.72

> -1.00

> -0.41

> 0.70

> -0.37

> -0.35

> -0.15

2007

> 2.40

> 7.50

> 0.07

> 1.40

> 2.30

> -1.50

> -0.82

> -0.27

> -0.72

> 0.14

> 0.28

> 0.19

> 0.13

2008

Fund Classification

Money Market USD

Source: Own calculations

77

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

Table 19: Sortino Ratio – Threshold Values for 1st Quartile Funds (very good)

Money Market EUR

Corporate Bonds USD

Corporate Bonds GBP

Corporate Bonds EUR

Equity Small Cap US

Equity Small Cap UK

Equity Small Cap Europe

Equity US

Equity UK

Equity Germany

Equity Europe

3.20 to 1.00

3.00 to -0.16

N/A

-0.61 to -0.98

1.10 to 0.20

N/A

0.97 to -0.12

-1.30 to -1.60

0.06 to -0.61

0.56 to -1.40

-0.43 to -0.85

0.04 to -0.25

0.41 to 0.01

1998

3.60 to 0.16

5.00 to -0.02

N/A

0.40 to -0.44

-0.08 to -0.48

N/A

2.60 to 0.59

6.20 to 4.30

6.30 to 4.50

0.54 to -0.90

1.50 to 0.35

-0.27 to -0.52

2.60 to 1.40

1999

4.00 to 0.93

3.10 to -1.50

N/A

0.86 to -0.15

-1.10 to -1.50

N/A

-0.37 to -1.10

1.30 to 0.80

0.96 to 0.48

1.10 to -0.10

1.10 to 0.54

0.74 to 0.41

0.68 to -0.10

2000

21.00 to 6.80

15.00 to 1.30

N/A

-0.73 to -1.70

-0.86 to -1.40

N/A

-0.30 to -1.70

0.31 to -0.25

-0.35 to -1.40

0.87 to -0.28

0.45 to -0.04

0.32 to 0.01

0.24 to -0.24

2001

10.00 to 2.50

21.00 to 2.10

12.00 to 4.5

-0.46 to -1.40

-0.33 to -0.80

0.14 to -0.43

0.09 to -1.10

0.39 to -0.24

0.86 to 0.06

1.30 to -0.11

0.23 to -0.08

0.55 to 0.20

0.46 to -0.11

2002

24.00 to 4.10

23.00 to 3.20

33.00 to 8.30

-0.01 to -1.60

-0.29 to -1.10

-0.53 to -1.30

0.84 to -0.33

2.60 to 1.90

2.90 to 2.20

0.65 to -0.35

1.10 to 0.44

0.20 to -0.05

-0.19 to -0.66

2003

7.10 to 0.05

14.00 to 1.80

32.00 to 8.90

-0.36 to -1.1

0.11 to -0.70

-1.40 to -2.00

-1.00 to -1.50

2.70 to 1.90

3.30 to 2.30

0.29 to -0.57

0.78 to 0.14

-0.21 to -0.41

0.78 to 0.03

2004

2.10 to -1.30

77.00 to 3.70

32.00 to 6.70

-0.12 to -0.64

-0.28 to -1.30

-0.59 to -1.10

-0.08 to -0.84

0.70 to -0.02

2.80 to 2.00

0.95 to -0.14

0.50 to -0.02

-0.03 to -0.33

1.60 to 0.92

2005

4.60 to 0.39

42.00 to 2.00

11.00 to 2.20

0.00 to -0.80

-0.13 to -0.77

0.44 to -0.02

-0.66 to -1.10

2.50 to 1.80

2.50 to 1.90

-0.54 to -1.10

0.95 to 0.39

0.11 to -0.13

1.30 to 0.75

2006

3.30 to -0.16

8.30 to 0.03

0.87 to -1.30

0.84 to 0.05

0.52 to -0.54

1.10 to -0.15

0.72 to -0.35

-1.00 to -1.50

-0.41 to -0.92

0.70 to -0.43

-0.37 to -0.84

-0.35 to -0.59

-0.15 to -0.73

2007

2.40 to -1.80

7.50 to -0.70

0.07 to -2.10

1.40 to -0.79

2.30 to 0.07

-1.50 to -2.70

-0.82 to -1.80

-0.27 to -0.59

-0.72 to -1.30

0.14 to -0.52

0.28 to -0.09

0.19 to -0.24

0.13 to -0.44

2008

Fund Classification

Money Market GBP

78

Money Market USD

Source: Own calculations

Copyright © 2010. Diplomica Verlag. All rights reserved.

Fund Performance Measurement

Table 20: Sortino Ratio – Threshold Values for 2nd Quartile Funds (good)

Fund Performance Measurement

Table 21: Correlation of the Information Ratio With Other Performance Measures Ranking comparison

Pearson

Lin’s

Cohen’s

Spearman’s

correlation

concordance

kappa

roh

Equity US Funds in year 1998 (N = 970 funds) IR vs. Alpha

0.7040

0.0947a

0.6888

0.8619

IR vs. Sharpe Ratio

0.7561

0.2659

0.6058

0.7920

IR vs. Sortino Ratio

0.9497

0.8656

0.9087

0.9809

0.2003

0.4979

a

0.7125a

0.7718

0.2322

0.7884

0.9331

a

a

a

0.4691a

IR vs. modified IR

0.6192

a

Equity US Funds in year 2008 (N = 3,953 funds) IR vs. Alpha

0.0292

0.2894

IR vs. Sharpe Ratio

0.0500

IR vs. Sortino Ratio

0.9768

0.8605

0.9696

0.9954

IR vs. modified IR

0.8147

0.5268

0.6658

0.8428

Source: Own calculations a Lowest value for the respective correlation coefficient

Table 22: Return Distribution of the S&P 500 Index (Timeframe: 1998 until 2008) Measure

Daily Data

Weekly Data

Monthly Data

0.0098

0.0065

0.0007

0.2073

0.1920

0.1636

Skewness

-0.1623

-1.2177

-0.8582

Kurtosis

11.6360

15.5941

4.8608

Meana Standard Deviation

a

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations a Mean and standard deviation annualized for better comparability

79

Fund Performance Measurement

Table 23: Performance Persistence of Equity and Equity Small Cap Funds Period

TOP 25% … years in a row 1 Year

TOP 50% … years in a row

2 Years

3 Years

1 Year

2 Years

3 Years

Equity Europe Funds 2008 to 2006

19.34%

4.93%

0.74%

22.41%

16.75%

10.84%

2007 to 2005

20.78%

1.74%

2.47%

26.74%

5.67%

17.59%

2006 to 2004

12.68%

7.79%

4.53%

15.58%

13.59%

20.83%

Equity Germany Funds 2008 to 2006

21.25%

2.50%

1.25%

27.50%

16.25%

6.25%

2007 to 2005

19.18%

1.37%

4.11%

20.55%

6.85%

21.92%

2006 to 2004

11.43%

2.86%

10.00%

15.71%

14.29%

20.00%

2008 to 2006

16.11%

7.29%

1.52%

19.30%

17.02%

13.68%

2007 to 2005

19.30%

1.93%

3.68%

27.54%

6.49%

15.67%

2006 to 2004

16.54%

4.67%

3.70%

22.57%

9.34%

18.09%

2008 to 2006

21.73%

2.33%

0.93%

25.73%

11.58%

12.67%

2007 to 2005

20.41%

2.88%

1.72%

28.22%

7.81%

13.94%

2006 to 2004

18.77%

3.04%

3.18%

26.48%

5.51%

17.99%

Equity UK Funds

Equity US Funds

Equity Small Cap Europe Funds 2008 to 2006

12.50%

9.24%

3.26%

24.46%

16.85%

8.70%

2007 to 2005

21.71%

3.29%

0.00%

31.58%

5.92%

12.50%

2006 to 2004

17.42%

5.30%

1.52%

22.73%

10.61%

15.91%

Equity Small Cap UK Funds 2008 to 2006

14.96%

4.72%

5.51%

23.62%

11.81%

14.17%

2007 to 2005

15.32%

1.80%

8.11%

27.03%

6.31%

16.22%

2006 to 2004

11.93%

10.09%

2.75%

12.84%

12.84%

23.85%

Copyright © 2010. Diplomica Verlag. All rights reserved.

Equity Small Cap US Funds 2008 to 2006

20.04%

2.29%

2.68%

27.48%

9.97%

12.55%

2007 to 2005

15.75%

4.73%

4.50%

24.99%

6.46%

18.52%

2006 to 2004

17.31%

4.30%

3.39%

23.06%

8.96%

17.98%

Source: Own calculations

80

Fund Performance Measurement

Table 24: Performance Persistence of Corporate Bond Funds Period

TOP 25% … years in a row 1 Year

TOP 50% … years in a row

2 Years

3 Years

1 Year

2 Years

3 Years

Corporate Bond EUR Funds 2008 to 2006

12.28%

4.09%

8.77%

18.71%

8.19%

22.81%

2007 to 2005

12.58%

5.96%

6.62%

14.57%

13.25%

21.85%

2006 to 2004

12.40%

7.75%

4.65%

16.28%

6.20%

27.13%

Corporate Bond GBP Funds 2008 to 2006

11.37%

7.11%

6.64%

13.27%

13.27%

23.22%

2007 to 2005

8.56%

1.60%

14.97%

16.04%

9.09%

24.60%

2006 to 2004

7.78%

1.80%

15.57%

16.17%

4.19%

29.34%

Corporate Bond USD Funds 2008 to 2006

13.42%

10.82%

0.87%

16.02%

19.05%

14.72%

2007 to 2005

19.91%

2.37%

2.84%

26.54%

6.64%

16.59%

2006 to 2004

17.24%

1.97%

5.91%

18.72%

6.40%

24.63%

Copyright © 2010. Diplomica Verlag. All rights reserved.

Source: Own calculations

81

Fund Performance Measurement

Appendix B Q1

Fragebogen Performance Analyse: Portfolio Manager

Name: Position: Unternehmen: Berufserfahrung:

TR Portfolio Management ----15 Jahre

Wie viele verschiedene Fonds verwalten Sie aktuell? 17 Fonds Welche Art von Anlegern investieren in Ihren Fond / in Ihre Fonds? Banken, Gemeinnützige Organisationen, Institutionen ohne Gewinnerzielungsabsicht In welche Anlageklasse(n) investieren Ihre Fonds? Fonds mit ausschließlich kurzen EUR-Renten bis 100% Aktienfonds Welcher Benchmark wird für den/die jeweiligen Fonds verwendet? Diverse: Index-Benchmarks, Absolute Return, Absolute Return auf Basis Wertuntergrenze In welcher Form / mit welchen Kennzahlen wird Ihre Leistung als Portfolio Manager aktuell bewertet? Extern: Vorgabe des Anlegers, Vergleich des Anlegers mit anderen Mandaten Intern: CPPI Benchmark (bei Mandaten mit Wertuntergrenze), Index-Benchmark In welchen zeitlichen Abständen erfolgt diese Bewertung? Monatlich

Copyright © 2010. Diplomica Verlag. All rights reserved.

Welche Stärken und Schwächen sehen Sie in der aktuellen Methode der Performance Analyse? Bildet diese Methode Ihre Leistung Ihrer Meinung nach objektiv ab? Schwäche: CPPI-Benchmark ist oft später ausgestoppt als reales Portfolio; Index-Benchmark entspricht in Abschwungphasen nicht immer der Risikotragfähigkeit des Anlegers; dann Diskussion über Benchmarkwechsel Stärke: Vergleich mit Index-Benchmarks problemlos täglich möglich Ist der Information Ratio Ihrer Meinung nach eine geeignete Kennzahl, um Ihre Leistung als Portfolio Manager abzubilden? Ist der Information Ratio Ihrer Meinung nach für Ihre Anlageklasse(n) überhaupt eine geeignete Maßzahl? Bei negativem Zähler ist die Aussagekraft eingeschränkt. Ansonsten ist den meisten unserer Anlegern der TE egal, das heißt im Fokus steht lediglich die Überrendite. Würden Sie Ihre Anlageentscheidungen bzw. die dahinterstehenden Methoden wesentlich ändern, wenn der Information Ratio als einzige Kennzahl zur Bewertung Ihrer Leistung herangezogen würde? Nein. Begründung siehe vorherige Frage.

82

Fund Performance Measurement

Q2

Fragebogen Performance Analyse: Portfolio Manager

Name: Position: Unternehmen: Berufserfahrung:

BK Portfolio Management ----20 Jahre

Wie viele verschiedene Fonds verwalten Sie aktuell? Mittelbar als verantwortlicher Gruppenleiter ca. 70, unmittelbar ca. 10 Fonds Welche Art von Anlegern investieren in Ihren Fond / in Ihre Fonds? Versicherungen, Industrieunternehmen, Banken, kirchliche Investoren In welche Anlageklasse(n) investieren Ihre Fonds? Aktien, Renten, Derivate, Fonds, Devisen Welcher Benchmark wird für den/die jeweiligen Fonds verwendet? Sehr unterschiedlich: Von symmetrischen gemischten und reinen Benchmarks über Wertsicherungskonzepten mit CPPI-Benchmark oder Ertragsvorgaben bis hin zu CashFlow basierten Benchmarks (Management gegen eine gegebene Liability Struktur) In welcher Form / mit welchen Kennzahlen wird Ihre Leistung als Portfolio Manager aktuell bewertet? Outperformance-Quote, Kundenzufriedenheit, Peer Group Vergleich In welchen zeitlichen Abständen erfolgt diese Bewertung? Kann quasi täglich ermittelt werden. Zur Beurteilung der Leistung erfolgt das Screening zum Monats- und final zum Jahresende (November oder Dezember)

Copyright © 2010. Diplomica Verlag. All rights reserved.

Welche Stärken und Schwächen sehen Sie in der aktuellen Methode der Performance Analyse? Bildet diese Methode Ihre Leistung Ihrer Meinung nach objektiv ab? Grundsätzlich in der angegebenen Mischung OK, es fehlt jedoch die längerfristige, risikoadjustierte Betrachtung. Ist der Information Ratio Ihrer Meinung nach eine geeignete Kennzahl, um Ihre Leistung als Portfolio Manager abzubilden? Ist der Information Ratio Ihrer Meinung nach für Ihre Anlageklasse(n) überhaupt eine geeignete Maßzahl? Konzeptionell bieten beide Performance-Maße (Sharpe Ratio und Information Ratio) ein breites Spektrum an Kritikmöglichkeiten. Insbesondere die Entscheidung Aufgrund negativer Werte, die durch einen negativen Zähler ausgelöst werden sind bei beiden Maßen stark Interpretationsbedürftig. Auch die Möglichkeit über eine bewusst passivere Steuerung des Fonds das IR hoch zu fahren ist aus Kundensicht sehr kritisch zu beurteilen. Ein Versuch die Vorteile von beiden Maßen zu nutzen könnte durch einen integrierten Ansatz realisiert werden. So könnte man z.B. die Summe aus SR und IR bilden oder die SR der Benchmark von dem SR des Fonds subtrahieren. Leider können dadurch nicht alle Probleme gelöst werden. Trotzdem wäre es gut, wenn möglich, beide Maße mit in Betrachtung einfließen zu lassen.

83

Fund Performance Measurement

Für eine Entweder / Oder Betrachtung würde ich das IR gegenüber der SR bevorzugen, da diese die Entwicklung der Benchmark in geeigneter Weise mit in die Berechnung einbezieht und so die aktive Managementleistung vergleichbar macht. Gerade für verschiedene Fonds und Asset-Klassen stellt es einen großen Vorteil dar. Um die oben beschriebene Verfehlung der Anreizstruktur zu verhindern würde eine Nebenbedingung in der Form: Trackking Error (annualisiert) muss größer gleich 3% sein, Sinn machen. Dies stellt allgemein einen Wert für aktives und indexnahes Management da und garantiert somit ein weiterhin aktives Management im Sinne des Kunden.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Würden Sie Ihre Anlageentscheidungen bzw. die dahinterstehenden Methoden wesentlich ändern, wenn der Information Ratio als einzige Kennzahl zur Bewertung Ihrer Leistung herangezogen würde? Ich persönlich nicht. Der Trend zu einem eher passiven Portfolio könnte aber entstehen. Damit wäre ein wesentliches Unterscheidungsmerkmal zu Wettbewerbern gefährdet

84

Fund Performance Measurement

Q3

Fragebogen Performance Analyse: Portfolio Manager

Name: Position: Unternehmen: Berufserfahrung:

TB Geschäftsführung ----19 Jahre

Wie viele verschiedene Fonds verwalten Sie aktuell? Einen Fond direkt, verantwortlich für 380 Fonds Welche Art von Anlegern investieren in Ihren Fond / in Ihre Fonds? Banken, VAG-Anleger, Unternehmen, Privatanleger, Non-Profits In welche Anlageklasse(n) investieren Ihre Fonds? Alle vom VAG zugelassenen Anlageklassen Welcher Benchmark wird für den/die jeweiligen Fonds verwendet? Indizes / Indexkombinationen für relative Mandate Schattenportfolios / Geldmarkt-plus / über Optionen abgesicherte Indexkombinationen für asymmetrische Mandate In welcher Form / mit welchen Kennzahlen wird Ihre Leistung als Portfolio Manager aktuell bewertet? Outperformance-Quote In welchen zeitlichen Abständen erfolgt diese Bewertung? Jährlich mit unterjährigen Reviews bei Bedarf

Copyright © 2010. Diplomica Verlag. All rights reserved.

Welche Stärken und Schwächen sehen Sie in der aktuellen Methode der Performance Analyse? Bildet diese Methode Ihre Leistung Ihrer Meinung nach objektiv ab? Da Sondereinflüsse bei der Performance-Berechnung berücksichtigt werden, ja. Starke Underperformance wird in einem separaten Leistungsbeurteilungspunkt „FondsHandling“ berücksichtigt. Ist der Information Ratio Ihrer Meinung nach eine geeignete Kennzahl, um Ihre Leistung als Portfolio Manager abzubilden? Ist der Information Ratio Ihrer Meinung nach für Ihre Anlageklasse(n) überhaupt eine geeignete Maßzahl? Für asymmetrische nicht geeignet. Dafür evtl. Sortino. Entscheidende Frage für symmetrische Mandate: Wann ist eine IR gut, wann sehr gut, wann schlecht? Muss meines Erachtens für jede Asset-Klasse unterschiedlich sein, je nachdem wie groß die Handlungsspielräume zur Nutzung von Breadth gemäß Fundamental Law of Active Management sind. Zur Festlegung der relevanten Schwellenwerte müsste eine theoretische Ableitung her. Eine reine Ableitung aus der Vergangenheit liefert rein empirische Wert, die z.B. vor und nach Subprime anders ausfallen können. Darüber hinaus dürften sich die kurzen Betrachtungszeiträume (aktuell 1 Jahr, aber ebenfalls 3 Jahre) mit der statistischen Signifikanz beißen.

85

Fund Performance Measurement

Copyright © 2010. Diplomica Verlag. All rights reserved.

Würden Sie Ihre Anlageentscheidungen bzw. die dahinterstehenden Methoden wesentlich ändern, wenn der Information Ratio als einzige Kennzahl zur Bewertung Ihrer Leistung herangezogen würde? Sicherlich würden die aktiven Wetten benchmarknäher ausfallen. Falls ein Fondsmanager die Systematik nicht gleich durchschaut, werden es ihm mit sicherlich innerhalb kürzester Zeit seine Kollegen sagen.

86

Fund Performance Measurement

Q4

Fragebogen Performance Analyse: Portfolio Manager

Name: Position: Unternehmen: Berufserfahrung:

AP Portfolio Management ----9 Jahre

Wie viele verschiedene Fonds verwalten Sie aktuell? 9 Fonds Welche Art von Anlegern investieren in Ihren Fond / in Ihre Fonds? Banken, Pensionskassen, Privatanleger In welche Anlageklasse(n) investieren Ihre Fonds? Überwiegend Renten, Aktienquoten ca. 10% Welcher Benchmark wird für den/die jeweiligen Fonds verwendet? Symmetrische Benchmarks (Indexkombinationen), bei wertgesicherten Fonds laufzeitkongruente Anleihen In welcher Form / mit welchen Kennzahlen wird Ihre Leistung als Portfolio Manager aktuell bewertet? Performancemessung relativ zur Benchmark In welchen zeitlichen Abständen erfolgt diese Bewertung? Tägliche Bewertung, Jahresultimo entscheidend

Copyright © 2010. Diplomica Verlag. All rights reserved.

Welche Stärken und Schwächen sehen Sie in der aktuellen Methode der Performance Analyse? Bildet diese Methode Ihre Leistung Ihrer Meinung nach objektiv ab? Schwäche: Der nur letzte Bewertungstag ist entscheidend. Stärke: Leicht messbar und dem Kunden vermittelbar. Ist der Information Ratio Ihrer Meinung nach eine geeignete Kennzahl, um Ihre Leistung als Portfolio Manager abzubilden? Ist der Information Ratio Ihrer Meinung nach für Ihre Anlageklasse(n) überhaupt eine geeignete Maßzahl? Halte ich für ungeeignet in Spezialfonds, da Benchmark eher als Vergleichsmaßstab vom Kunden gesehen wird und keine unbedingte Nachbildung verlangt wird. Aktives Management als Kundennutzen geht verloren. Der Kunde könnte dann auf Indexfonds ausweichen. Die Benchmarks sind oft mit den Volumina in Institutionellen Fonds nicht sinnvoll abzubilden. Dadurch würde die Kennzahl stark verfälscht. Würden Sie Ihre Anlageentscheidungen bzw. die dahinterstehenden Methoden wesentlich ändern, wenn der Information Ratio als einzige Kennzahl zur Bewertung Ihrer Leistung herangezogen würde? Ja. Der Information Ratio würde bewirken, dass die Benchmark noch enger abgebildet wird.

87

Fund Performance Measurement

Q5

Fragebogen Performance Analyse: Leiter Performance Analyse

Name: Position: Unternehmen: Berufserfahrung:

MK Abteilungsleitung – Performance Analyse ----15 Jahre

Welche Datenbanken / Informationssysteme nutzen Sie zurzeit als Basis zur Performance Analyse? Fondsbuchhaltungssystem: Multifonds Zeitreihenanalysesystem: Asset Control Data Warehouse: Business Objects Attribution: StatPro Attribution und Eigenentwicklung Composite: StatPro Composites Wettbewerbsanalysen: Eigenentwicklung zusätzlich: Middle Ware (EAI)

Copyright © 2010. Diplomica Verlag. All rights reserved.

Wie ist die Performance Analyse aktuell aufgebaut? Welche Kennzahlen kommen dabei zur Anwendung? Performance-Messung: Returnkennzahlen, relative Returns (Fonds, Benchmark), täglich, brutto und netto Performancekennzahlen (Information Ratio als führende Kennzahl), täglich, brutto und netto GIPS Composites

Performance-Attribution:

Returns, Gewichte, Returnbeiträge, Allokations-, Selektions-, Währungsbeiträge, spezielle Beiträge für die Vermögensverwaltungs- und Dachfondsmandate (z.B. Einfluss Zielfondsmanagement) und Wertsicherungskonzepte Performance-Contribution: Returns, Gewichte, Returnbeiträge jeweils auf Tagesbasis und Einzeltitelebene, sowie verschiedene Segmentierungen (Laufzeit, Länder, Branchen, Währungen, Ratings etc.)

Wettbewerbsanalyse:

Kennzahlen bzgl. Peergroup-Rankings, wie z. B.: Quantile, Perzentile auf Einzelfonds bezogen und über Gruppen aggregiert. Eingruppierung der Benchmark zu Vergleichszwecken möglich.

Unterscheidet sich die Methodik je nach Anlageschwerpunkt des Fonds? Wenn ja, wie? Unterschiede bei der Attribution, verursacht durch die unterschiedlichen Fondstypen, Assetklassen und Investmentprozesse. Unterscheidung der symmetrischen und asymmetrischen Portfolios bei der Performancemessung. Welche Rolle spielt die Performance Historie über die letzten zwei, drei Jahre hinweg bei der Leistungsbewertung eines Managers? Neben den 1-jährigen Ergebnissen werden gleichwertig 3-jährige Ergebnisse berücksichtigt.

88

Fund Performance Measurement

Vergleichen Sie das Rendite/Risiko Profil der Fonds Ihres Unternehmens mit einer Vergleichsgruppe anderer Fonds, die den gleichen Anlageschwerpunkt haben? Ist der relative Vergleich besser/schlechter als eine absolute Bewertung? Für den Vertrieb ist das Monitoring der absoluten Performance und des Rendite / Risikoprofils eines Fonds wichtig, denn für den Retail-Kunden zählt in erster Linie die absolute Performance. Zum internen Controlling und der Beurteilung der Fondsmanagerleistung ist der relative Vergleich wichtig. Die interne Bewertung ist vom Auftrag des Fonds abgeleitet, der in einer passenden Benchmark quantifiziert wird. Die relative Bewertung gegenüber Peers spiegelt die Kundensicht und zeigt die Wettbewerbsfähigkeit unseres Produktprogramms. Wir vergleichen daher unsere Publikumsfonds mit entsprechenden Hauptwettbewerberfonds, aber auch mit den Peer-Groups von Morningstar, Feri und Lipper. Die Rendite / Risiko-Profile unserer Fonds und fremder Fonds werden vergleichbar gemacht und auch monatlich verglichen. Welche Stärken und Schwächen sehen Sie in der aktuellen Methode der Performance Analyse? Stärken: Bei ausreichendem Datenmaterial und Kenntnis des Investmentprozesses sind die Analysemöglichkeiten absolut, sowie relativ zur Benchmark und Peer-Group für Relative Return Produkte gut. Die Einführung einer Fixed Income Attribution ist geplant.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Schwächen:

Die Analysemöglichkeiten für Absolut- und Total Return-Produkte sind deutlich eingeschränkt. Es fehlen geeignete Vergleichsmaßstäbe, Attributionsmodelle (Ausnahme Wertsicherungskonzepte: IMMUNOs) und standardisierte Risikokennzahlen.

Arbeiten Sie häufig mit dem Information Ratio? Ist der Information Ratio Ihrer Meinung nach eine geeignete Kennzahl, um die Leistung eines Portfolio Managers abzubilden? Ist der Information Ratio Ihrer Meinung nach für alle Anlageklasse(n) gleichermaßen geeignet? Wir arbeiten mit dem IR und halten es für einen geeigneten Beurteilungsmaßstab. Es ist unseres Erachtens für alle Anlageklassen geeignet, bei denen die aktiven Renditen annähernd normalverteilt sind. Es gibt jedoch wichtige Voraussetzungen, die wir vor der Implementierung des Information Ratio erfüllt haben: 1. Allen Fonds muss eine fondsprofiladäquate Benchmark zugewiesen sein. 2. Bewertungszeitpunkte von Fonds und Benchmark müssen übereinstimmen 3. Zur Beurteilung der Portfoliomanagerleistung ist eine Bereinigung der Fondsperformance um alle Kostenbestandteile vorzunehmen, die vom Portfoliomanager nicht zu vertreten sind (hauptsächlich Verwaltungsvergütung, Depotbankvergütung, Performance-Fees, Veröffentlichungs- und Prüfkosten).

89

Fund Performance Measurement

Haben Sie bereits einmal mit dem Sortino Ratio oder einer vergleichbaren Kennzahl gearbeitet, die das sog. „downside risk“ bewertet? Wenn ja, welche Erfahrungen haben Sie damit gemacht? Wir arbeiten mit dem Sortino Ratio, zurzeit ist die Kennzahl aber noch nicht in unsere Standardsysteme (Asset Control, Datawareouse) integriert. Erfahrungen in der Massenanwendung fehlen also noch. Wir möchten die Kennzahl gerne als Beurteilungsmaßstab für asymmetrische Fondskonzepte einsetzen, falls sich bei noch durchzuführenden Tests herausstellen sollte, dass auch die aktiven Renditen der asymmetrischen Fonds asymmetrisch verteilt sind. Welche Daten-Intervalle (täglich, wöchentlich, monatlich) verwenden Sie üblicherweise zur Berechnung der Performance Kennzahlen? Gibt es aus praktischer Sicht hier Restriktionen? Die meisten Performancekennzahlen werden wöchentlich gerechnet. Durch die Umstellung auf Schlusskursbewertung und die Verfügbarkeit von Brutto-Returns wäre dies aber nicht mehr zwingend und könnte mit höherer Frequenz erfolgen. Zur Berechnung des IR verwenden wir Wochendaten. Die Verwendung von Tagesdaten erschien uns zu hochfrequent, weil Restverzerrungen und Datenungenauigkeiten eine stark verzerrende Wirkung auf das IR ausüben könnten. Aktuell werden aktive Renditen und Tracking Errors (TE) täglich mit Wochendaten berechnet und es werden rollierende Durchschnitte über die letzten 5 täglich ermittelten Werte gebildet, um eine Glättung herbeizuführen (Grund für die Glättung ist unsere Beobachtung, dass TE Tagesmuster aufweisen können, d. h. der Erfassungstag des auf wöchentlichem Daten-Intervall ermittelten TE (Mo, Di, Mi, Do oder Fr) hat einen Einfluss auf die Höhe des TE. Performance- und Attributions-Analysen beruhen auf täglichen Daten-Intervallen. Wettbewerbsanalysen liegen monatliche Datenintervalle zugrunde, da die RatingAgenturen nur Monatsdaten zur Verfügung stellen.

Copyright © 2010. Diplomica Verlag. All rights reserved.

Welche anderen, praktischen Aspekte können Probleme bei der Performance Analyse darstellen? Mangelnde qualitätsgesicherte Datenverfügbarkeit (insbesondere im Rentenbereich: Indizes, Risikokennzahlen, wie z.B. Greek Letters), Datenfehler, Schnittstellenprobleme etwa zum Buchhaltungssystem, Implementierungsprobleme komplexerer Kenzahlen in der Massenverarbeitung, niedrige Systemperformance, etc. Die Veränderungen bei den Produkten, weg vom Wertpapierbezogenen managen, hin zu verbundenen Strategien und Lösungen werden die nächsten Herausforderungen sein.

90

Unser gesamtes Verlagsprogramm finden Sie unter: www.diplomica-verlag.de

Copyright © 2010. Diplomica Verlag. All rights reserved.

Diplomica Verlag